Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/signal/__init__.py

@@ -0,0 +1,361 @@
+"""
+=======================================
+Signal processing (:mod:`scipy.signal`)
+=======================================
+
+Convolution
+===========
+
+.. autosummary::
+   :toctree: generated/
+
+   convolve           -- N-D convolution.
+   correlate          -- N-D correlation.
+   fftconvolve        -- N-D convolution using the FFT.
+   oaconvolve         -- N-D convolution using the overlap-add method.
+   convolve2d         -- 2-D convolution (more options).
+   correlate2d        -- 2-D correlation (more options).
+   sepfir2d           -- Convolve with a 2-D separable FIR filter.
+   choose_conv_method -- Chooses faster of FFT and direct convolution methods.
+
+B-splines
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   bspline        -- B-spline basis function of order n.
+   cubic          -- B-spline basis function of order 3.
+   quadratic      -- B-spline basis function of order 2.
+   gauss_spline   -- Gaussian approximation to the B-spline basis function.
+   cspline1d      -- Coefficients for 1-D cubic (3rd order) B-spline.
+   qspline1d      -- Coefficients for 1-D quadratic (2nd order) B-spline.
+   cspline2d      -- Coefficients for 2-D cubic (3rd order) B-spline.
+   qspline2d      -- Coefficients for 2-D quadratic (2nd order) B-spline.
+   cspline1d_eval -- Evaluate a cubic spline at the given points.
+   qspline1d_eval -- Evaluate a quadratic spline at the given points.
+   spline_filter  -- Smoothing spline (cubic) filtering of a rank-2 array.
+
+Filtering
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   order_filter  -- N-D order filter.
+   medfilt       -- N-D median filter.
+   medfilt2d     -- 2-D median filter (faster).
+   wiener        -- N-D Wiener filter.
+
+   symiirorder1  -- 2nd-order IIR filter (cascade of first-order systems).
+   symiirorder2  -- 4th-order IIR filter (cascade of second-order systems).
+   lfilter       -- 1-D FIR and IIR digital linear filtering.
+   lfiltic       -- Construct initial conditions for `lfilter`.
+   lfilter_zi    -- Compute an initial state zi for the lfilter function that
+                 -- corresponds to the steady state of the step response.
+   filtfilt      -- A forward-backward filter.
+   savgol_filter -- Filter a signal using the Savitzky-Golay filter.
+
+   deconvolve    -- 1-D deconvolution using lfilter.
+
+   sosfilt       -- 1-D IIR digital linear filtering using
+                 -- a second-order sections filter representation.
+   sosfilt_zi    -- Compute an initial state zi for the sosfilt function that
+                 -- corresponds to the steady state of the step response.
+   sosfiltfilt   -- A forward-backward filter for second-order sections.
+   hilbert       -- Compute 1-D analytic signal, using the Hilbert transform.
+   hilbert2      -- Compute 2-D analytic signal, using the Hilbert transform.
+
+   decimate      -- Downsample a signal.
+   detrend       -- Remove linear and/or constant trends from data.
+   resample      -- Resample using Fourier method.
+   resample_poly -- Resample using polyphase filtering method.
+   upfirdn       -- Upsample, apply FIR filter, downsample.
+
+Filter design
+=============
+
+.. autosummary::
+   :toctree: generated/
+
+   bilinear      -- Digital filter from an analog filter using
+                    -- the bilinear transform.
+   bilinear_zpk  -- Digital filter from an analog filter using
+                    -- the bilinear transform.
+   findfreqs     -- Find array of frequencies for computing filter response.
+   firls         -- FIR filter design using least-squares error minimization.
+   firwin        -- Windowed FIR filter design, with frequency response
+                    -- defined as pass and stop bands.
+   firwin2       -- Windowed FIR filter design, with arbitrary frequency
+                    -- response.
+   freqs         -- Analog filter frequency response from TF coefficients.
+   freqs_zpk     -- Analog filter frequency response from ZPK coefficients.
+   freqz         -- Digital filter frequency response from TF coefficients.
+   freqz_zpk     -- Digital filter frequency response from ZPK coefficients.
+   sosfreqz      -- Digital filter frequency response for SOS format filter.
+   group_delay   -- Digital filter group delay.
+   iirdesign     -- IIR filter design given bands and gains.
+   iirfilter     -- IIR filter design given order and critical frequencies.
+   kaiser_atten  -- Compute the attenuation of a Kaiser FIR filter, given
+                    -- the number of taps and the transition width at
+                    -- discontinuities in the frequency response.
+   kaiser_beta   -- Compute the Kaiser parameter beta, given the desired
+                    -- FIR filter attenuation.
+   kaiserord     -- Design a Kaiser window to limit ripple and width of
+                    -- transition region.
+   minimum_phase -- Convert a linear phase FIR filter to minimum phase.
+   savgol_coeffs -- Compute the FIR filter coefficients for a Savitzky-Golay
+                    -- filter.
+   remez         -- Optimal FIR filter design.
+
+   unique_roots  -- Unique roots and their multiplicities.
+   residue       -- Partial fraction expansion of b(s) / a(s).
+   residuez      -- Partial fraction expansion of b(z) / a(z).
+   invres        -- Inverse partial fraction expansion for analog filter.
+   invresz       -- Inverse partial fraction expansion for digital filter.
+   BadCoefficients  -- Warning on badly conditioned filter coefficients.
+
+Lower-level filter design functions:
+
+.. autosummary::
+   :toctree: generated/
+
+   abcd_normalize -- Check state-space matrices and ensure they are rank-2.
+   band_stop_obj  -- Band Stop Objective Function for order minimization.
+   besselap       -- Return (z,p,k) for analog prototype of Bessel filter.
+   buttap         -- Return (z,p,k) for analog prototype of Butterworth filter.
+   cheb1ap        -- Return (z,p,k) for type I Chebyshev filter.
+   cheb2ap        -- Return (z,p,k) for type II Chebyshev filter.
+   cmplx_sort     -- Sort roots based on magnitude.
+   ellipap        -- Return (z,p,k) for analog prototype of elliptic filter.
+   lp2bp          -- Transform a lowpass filter prototype to a bandpass filter.
+   lp2bp_zpk      -- Transform a lowpass filter prototype to a bandpass filter.
+   lp2bs          -- Transform a lowpass filter prototype to a bandstop filter.
+   lp2bs_zpk      -- Transform a lowpass filter prototype to a bandstop filter.
+   lp2hp          -- Transform a lowpass filter prototype to a highpass filter.
+   lp2hp_zpk      -- Transform a lowpass filter prototype to a highpass filter.
+   lp2lp          -- Transform a lowpass filter prototype to a lowpass filter.
+   lp2lp_zpk      -- Transform a lowpass filter prototype to a lowpass filter.
+   normalize      -- Normalize polynomial representation of a transfer function.
+
+
+
+Matlab-style IIR filter design
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   butter -- Butterworth
+   buttord
+   cheby1 -- Chebyshev Type I
+   cheb1ord
+   cheby2 -- Chebyshev Type II
+   cheb2ord
+   ellip -- Elliptic (Cauer)
+   ellipord
+   bessel -- Bessel (no order selection available -- try butterod)
+   iirnotch      -- Design second-order IIR notch digital filter.
+   iirpeak       -- Design second-order IIR peak (resonant) digital filter.
+
+Continuous-time linear systems
+==============================
+
+.. autosummary::
+   :toctree: generated/
+
+   lti              -- Continuous-time linear time invariant system base class.
+   StateSpace       -- Linear time invariant system in state space form.
+   TransferFunction -- Linear time invariant system in transfer function form.
+   ZerosPolesGain   -- Linear time invariant system in zeros, poles, gain form.
+   lsim             -- Continuous-time simulation of output to linear system.
+   lsim2            -- Like lsim, but `scipy.integrate.odeint` is used.
+   impulse          -- Impulse response of linear, time-invariant (LTI) system.
+   impulse2         -- Like impulse, but `scipy.integrate.odeint` is used.
+   step             -- Step response of continuous-time LTI system.
+   step2            -- Like step, but `scipy.integrate.odeint` is used.
+   freqresp         -- Frequency response of a continuous-time LTI system.
+   bode             -- Bode magnitude and phase data (continuous-time LTI).
+
+Discrete-time linear systems
+============================
+
+.. autosummary::
+   :toctree: generated/
+
+   dlti             -- Discrete-time linear time invariant system base class.
+   StateSpace       -- Linear time invariant system in state space form.
+   TransferFunction -- Linear time invariant system in transfer function form.
+   ZerosPolesGain   -- Linear time invariant system in zeros, poles, gain form.
+   dlsim            -- Simulation of output to a discrete-time linear system.
+   dimpulse         -- Impulse response of a discrete-time LTI system.
+   dstep            -- Step response of a discrete-time LTI system.
+   dfreqresp        -- Frequency response of a discrete-time LTI system.
+   dbode            -- Bode magnitude and phase data (discrete-time LTI).
+
+LTI representations
+===================
+
+.. autosummary::
+   :toctree: generated/
+
+   tf2zpk        -- Transfer function to zero-pole-gain.
+   tf2sos        -- Transfer function to second-order sections.
+   tf2ss         -- Transfer function to state-space.
+   zpk2tf        -- Zero-pole-gain to transfer function.
+   zpk2sos       -- Zero-pole-gain to second-order sections.
+   zpk2ss        -- Zero-pole-gain to state-space.
+   ss2tf         -- State-pace to transfer function.
+   ss2zpk        -- State-space to pole-zero-gain.
+   sos2zpk       -- Second-order sections to zero-pole-gain.
+   sos2tf        -- Second-order sections to transfer function.
+   cont2discrete -- Continuous-time to discrete-time LTI conversion.
+   place_poles   -- Pole placement.
+
+Waveforms
+=========
+
+.. autosummary::
+   :toctree: generated/
+
+   chirp        -- Frequency swept cosine signal, with several freq functions.
+   gausspulse   -- Gaussian modulated sinusoid.
+   max_len_seq  -- Maximum length sequence.
+   sawtooth     -- Periodic sawtooth.
+   square       -- Square wave.
+   sweep_poly   -- Frequency swept cosine signal; freq is arbitrary polynomial.
+   unit_impulse -- Discrete unit impulse.
+
+Window functions
+================
+
+For window functions, see the `scipy.signal.windows` namespace.
+
+In the `scipy.signal` namespace, there is a convenience function to
+obtain these windows by name:
+
+.. autosummary::
+   :toctree: generated/
+
+   get_window -- Return a window of a given length and type.
+
+Wavelets
+========
+
+.. autosummary::
+   :toctree: generated/
+
+   cascade      -- Compute scaling function and wavelet from coefficients.
+   daub         -- Return low-pass.
+   morlet       -- Complex Morlet wavelet.
+   qmf          -- Return quadrature mirror filter from low-pass.
+   ricker       -- Return ricker wavelet.
+   morlet2      -- Return Morlet wavelet, compatible with cwt.
+   cwt          -- Perform continuous wavelet transform.
+
+Peak finding
+============
+
+.. autosummary::
+   :toctree: generated/
+
+   argrelmin        -- Calculate the relative minima of data.
+   argrelmax        -- Calculate the relative maxima of data.
+   argrelextrema    -- Calculate the relative extrema of data.
+   find_peaks       -- Find a subset of peaks inside a signal.
+   find_peaks_cwt   -- Find peaks in a 1-D array with wavelet transformation.
+   peak_prominences -- Calculate the prominence of each peak in a signal.
+   peak_widths      -- Calculate the width of each peak in a signal.
+
+Spectral analysis
+=================
+
+.. autosummary::
+   :toctree: generated/
+
+   periodogram    -- Compute a (modified) periodogram.
+   welch          -- Compute a periodogram using Welch's method.
+   csd            -- Compute the cross spectral density, using Welch's method.
+   coherence      -- Compute the magnitude squared coherence, using Welch's method.
+   spectrogram    -- Compute the spectrogram.
+   lombscargle    -- Computes the Lomb-Scargle periodogram.
+   vectorstrength -- Computes the vector strength.
+   stft           -- Compute the Short Time Fourier Transform.
+   istft          -- Compute the Inverse Short Time Fourier Transform.
+   check_COLA     -- Check the COLA constraint for iSTFT reconstruction.
+   check_NOLA     -- Check the NOLA constraint for iSTFT reconstruction.
+
+"""
+from . import sigtools, windows
+from .waveforms import *
+from ._max_len_seq import max_len_seq
+from ._upfirdn import upfirdn
+
+# The spline module (a C extension) provides:
+#     cspline2d, qspline2d, sepfir2d, symiirord1, symiirord2
+from .spline import *
+
+from .bsplines import *
+from .filter_design import *
+from .fir_filter_design import *
+from .ltisys import *
+from .lti_conversion import *
+from .signaltools import *
+from ._savitzky_golay import savgol_coeffs, savgol_filter
+from .spectral import *
+from .wavelets import *
+from ._peak_finding import *
+from .windows import get_window  # keep this one in signal namespace
+
+
+# deal with * -> windows.* doc-only soft-deprecation
+deprecated_windows = ('boxcar', 'triang', 'parzen', 'bohman', 'blackman',
+                      'nuttall', 'blackmanharris', 'flattop', 'bartlett',
+                      'barthann', 'hamming', 'kaiser', 'gaussian',
+                      'general_gaussian', 'chebwin', 'slepian', 'cosine',
+                      'hann', 'exponential', 'tukey')
+
+# backward compatibility imports for actually deprecated windows not
+# in the above list
+from .windows import hanning
+
+
+def deco(name):
+    f = getattr(windows, name)
+    # Add deprecation to docstring
+
+    def wrapped(*args, **kwargs):
+        return f(*args, **kwargs)
+
+    wrapped.__name__ = name
+    wrapped.__module__ = 'scipy.signal'
+    if hasattr(f, '__qualname__'):
+        wrapped.__qualname__ = f.__qualname__
+
+    if f.__doc__:
+        lines = f.__doc__.splitlines()
+        for li, line in enumerate(lines):
+            if line.strip() == 'Parameters':
+                break
+        else:
+            raise RuntimeError('dev error: badly formatted doc')
+        spacing = ' ' * line.find('P')
+        lines.insert(li, ('{0}.. warning:: scipy.signal.{1} is deprecated,\n'
+                          '{0}             use scipy.signal.windows.{1} '
+                          'instead.\n'.format(spacing, name)))
+        wrapped.__doc__ = '\n'.join(lines)
+
+    return wrapped
+
+
+for name in deprecated_windows:
+    locals()[name] = deco(name)
+
+del deprecated_windows, name, deco
+
+
+__all__ = [s for s in dir() if not s.startswith('_')]
+
+from scipy._lib._testutils import PytestTester
+test = PytestTester(__name__)
+del PytestTester

venv/Lib/site-packages/scipy/signal/_arraytools.py

@@ -0,0 +1,241 @@
+"""
+Functions for acting on a axis of an array.
+"""
+import numpy as np
+
+
+def axis_slice(a, start=None, stop=None, step=None, axis=-1):
+    """Take a slice along axis 'axis' from 'a'.
+
+    Parameters
+    ----------
+    a : numpy.ndarray
+        The array to be sliced.
+    start, stop, step : int or None
+        The slice parameters.
+    axis : int, optional
+        The axis of `a` to be sliced.
+
+    Examples
+    --------
+    >>> a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+    >>> axis_slice(a, start=0, stop=1, axis=1)
+    array([[1],
+           [4],
+           [7]])
+    >>> axis_slice(a, start=1, axis=0)
+    array([[4, 5, 6],
+           [7, 8, 9]])
+
+    Notes
+    -----
+    The keyword arguments start, stop and step are used by calling
+    slice(start, stop, step). This implies axis_slice() does not
+    handle its arguments the exactly the same as indexing. To select
+    a single index k, for example, use
+        axis_slice(a, start=k, stop=k+1)
+    In this case, the length of the axis 'axis' in the result will
+    be 1; the trivial dimension is not removed. (Use numpy.squeeze()
+    to remove trivial axes.)
+    """
+    a_slice = [slice(None)] * a.ndim
+    a_slice[axis] = slice(start, stop, step)
+    b = a[tuple(a_slice)]
+    return b
+
+
+def axis_reverse(a, axis=-1):
+    """Reverse the 1-D slices of `a` along axis `axis`.
+
+    Returns axis_slice(a, step=-1, axis=axis).
+    """
+    return axis_slice(a, step=-1, axis=axis)
+
+
+def odd_ext(x, n, axis=-1):
+    """
+    Odd extension at the boundaries of an array
+
+    Generate a new ndarray by making an odd extension of `x` along an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> from scipy.signal._arraytools import odd_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> odd_ext(a, 2)
+    array([[-1,  0,  1,  2,  3,  4,  5,  6,  7],
+           [-4, -1,  0,  1,  4,  9, 16, 23, 28]])
+
+    Odd extension is a "180 degree rotation" at the endpoints of the original
+    array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = odd_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='odd extension')
+    >>> plt.plot(arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    if n > x.shape[axis] - 1:
+        raise ValueError(("The extension length n (%d) is too big. " +
+                         "It must not exceed x.shape[axis]-1, which is %d.")
+                         % (n, x.shape[axis] - 1))
+    left_end = axis_slice(x, start=0, stop=1, axis=axis)
+    left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
+    right_end = axis_slice(x, start=-1, axis=axis)
+    right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
+    ext = np.concatenate((2 * left_end - left_ext,
+                          x,
+                          2 * right_end - right_ext),
+                         axis=axis)
+    return ext
+
+
+def even_ext(x, n, axis=-1):
+    """
+    Even extension at the boundaries of an array
+
+    Generate a new ndarray by making an even extension of `x` along an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> from scipy.signal._arraytools import even_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> even_ext(a, 2)
+    array([[ 3,  2,  1,  2,  3,  4,  5,  4,  3],
+           [ 4,  1,  0,  1,  4,  9, 16,  9,  4]])
+
+    Even extension is a "mirror image" at the boundaries of the original array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = even_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='even extension')
+    >>> plt.plot(arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    if n > x.shape[axis] - 1:
+        raise ValueError(("The extension length n (%d) is too big. " +
+                         "It must not exceed x.shape[axis]-1, which is %d.")
+                         % (n, x.shape[axis] - 1))
+    left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis)
+    right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis)
+    ext = np.concatenate((left_ext,
+                          x,
+                          right_ext),
+                         axis=axis)
+    return ext
+
+
+def const_ext(x, n, axis=-1):
+    """
+    Constant extension at the boundaries of an array
+
+    Generate a new ndarray that is a constant extension of `x` along an axis.
+
+    The extension repeats the values at the first and last element of
+    the axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> from scipy.signal._arraytools import const_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> const_ext(a, 2)
+    array([[ 1,  1,  1,  2,  3,  4,  5,  5,  5],
+           [ 0,  0,  0,  1,  4,  9, 16, 16, 16]])
+
+    Constant extension continues with the same values as the endpoints of the
+    array:
+
+    >>> t = np.linspace(0, 1.5, 100)
+    >>> a = 0.9 * np.sin(2 * np.pi * t**2)
+    >>> b = const_ext(a, 40)
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(arange(-40, 140), b, 'b', lw=1, label='constant extension')
+    >>> plt.plot(arange(100), a, 'r', lw=2, label='original')
+    >>> plt.legend(loc='best')
+    >>> plt.show()
+    """
+    if n < 1:
+        return x
+    left_end = axis_slice(x, start=0, stop=1, axis=axis)
+    ones_shape = [1] * x.ndim
+    ones_shape[axis] = n
+    ones = np.ones(ones_shape, dtype=x.dtype)
+    left_ext = ones * left_end
+    right_end = axis_slice(x, start=-1, axis=axis)
+    right_ext = ones * right_end
+    ext = np.concatenate((left_ext,
+                          x,
+                          right_ext),
+                         axis=axis)
+    return ext
+
+
+def zero_ext(x, n, axis=-1):
+    """
+    Zero padding at the boundaries of an array
+
+    Generate a new ndarray that is a zero-padded extension of `x` along
+    an axis.
+
+    Parameters
+    ----------
+    x : ndarray
+        The array to be extended.
+    n : int
+        The number of elements by which to extend `x` at each end of the
+        axis.
+    axis : int, optional
+        The axis along which to extend `x`. Default is -1.
+
+    Examples
+    --------
+    >>> from scipy.signal._arraytools import zero_ext
+    >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]])
+    >>> zero_ext(a, 2)
+    array([[ 0,  0,  1,  2,  3,  4,  5,  0,  0],
+           [ 0,  0,  0,  1,  4,  9, 16,  0,  0]])
+    """
+    if n < 1:
+        return x
+    zeros_shape = list(x.shape)
+    zeros_shape[axis] = n
+    zeros = np.zeros(zeros_shape, dtype=x.dtype)
+    ext = np.concatenate((zeros, x, zeros), axis=axis)
+    return ext

venv/Lib/site-packages/scipy/signal/_max_len_seq.py

@@ -0,0 +1,137 @@
+# Author: Eric Larson
+# 2014
+
+"""Tools for MLS generation"""
+
+import numpy as np
+
+from ._max_len_seq_inner import _max_len_seq_inner
+
+__all__ = ['max_len_seq']
+
+
+# These are definitions of linear shift register taps for use in max_len_seq()
+_mls_taps = {2: [1], 3: [2], 4: [3], 5: [3], 6: [5], 7: [6], 8: [7, 6, 1],
+             9: [5], 10: [7], 11: [9], 12: [11, 10, 4], 13: [12, 11, 8],
+             14: [13, 12, 2], 15: [14], 16: [15, 13, 4], 17: [14],
+             18: [11], 19: [18, 17, 14], 20: [17], 21: [19], 22: [21],
+             23: [18], 24: [23, 22, 17], 25: [22], 26: [25, 24, 20],
+             27: [26, 25, 22], 28: [25], 29: [27], 30: [29, 28, 7],
+             31: [28], 32: [31, 30, 10]}
+
+def max_len_seq(nbits, state=None, length=None, taps=None):
+    """
+    Maximum length sequence (MLS) generator.
+
+    Parameters
+    ----------
+    nbits : int
+        Number of bits to use. Length of the resulting sequence will
+        be ``(2**nbits) - 1``. Note that generating long sequences
+        (e.g., greater than ``nbits == 16``) can take a long time.
+    state : array_like, optional
+        If array, must be of length ``nbits``, and will be cast to binary
+        (bool) representation. If None, a seed of ones will be used,
+        producing a repeatable representation. If ``state`` is all
+        zeros, an error is raised as this is invalid. Default: None.
+    length : int, optional
+        Number of samples to compute. If None, the entire length
+        ``(2**nbits) - 1`` is computed.
+    taps : array_like, optional
+        Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence).
+        If None, taps will be automatically selected (for up to
+        ``nbits == 32``).
+
+    Returns
+    -------
+    seq : array
+        Resulting MLS sequence of 0's and 1's.
+    state : array
+        The final state of the shift register.
+
+    Notes
+    -----
+    The algorithm for MLS generation is generically described in:
+
+        https://en.wikipedia.org/wiki/Maximum_length_sequence
+
+    The default values for taps are specifically taken from the first
+    option listed for each value of ``nbits`` in:
+
+        http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm
+
+    .. versionadded:: 0.15.0
+
+    Examples
+    --------
+    MLS uses binary convention:
+
+    >>> from scipy.signal import max_len_seq
+    >>> max_len_seq(4)[0]
+    array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8)
+
+    MLS has a white spectrum (except for DC):
+
+    >>> import matplotlib.pyplot as plt
+    >>> from numpy.fft import fft, ifft, fftshift, fftfreq
+    >>> seq = max_len_seq(6)[0]*2-1  # +1 and -1
+    >>> spec = fft(seq)
+    >>> N = len(seq)
+    >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    Circular autocorrelation of MLS is an impulse:
+
+    >>> acorrcirc = ifft(spec * np.conj(spec)).real
+    >>> plt.figure()
+    >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    Linear autocorrelation of MLS is approximately an impulse:
+
+    >>> acorr = np.correlate(seq, seq, 'full')
+    >>> plt.figure()
+    >>> plt.plot(np.arange(-N+1, N), acorr, '.-')
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    if taps is None:
+        if nbits not in _mls_taps:
+            known_taps = np.array(list(_mls_taps.keys()))
+            raise ValueError('nbits must be between %s and %s if taps is None'
+                             % (known_taps.min(), known_taps.max()))
+        taps = np.array(_mls_taps[nbits], np.intp)
+    else:
+        taps = np.unique(np.array(taps, np.intp))[::-1]
+        if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1:
+            raise ValueError('taps must be non-empty with values between '
+                             'zero and nbits (inclusive)')
+        taps = np.ascontiguousarray(taps)  # needed for Cython
+    n_max = (2**nbits) - 1
+    if length is None:
+        length = n_max
+    else:
+        length = int(length)
+        if length < 0:
+            raise ValueError('length must be greater than or equal to 0')
+    # We use int8 instead of bool here because NumPy arrays of bools
+    # don't seem to work nicely with Cython
+    if state is None:
+        state = np.ones(nbits, dtype=np.int8, order='c')
+    else:
+        # makes a copy if need be, ensuring it's 0's and 1's
+        state = np.array(state, dtype=bool, order='c').astype(np.int8)
+    if state.ndim != 1 or state.size != nbits:
+        raise ValueError('state must be a 1-D array of size nbits')
+    if np.all(state == 0):
+        raise ValueError('state must not be all zeros')
+
+    seq = np.empty(length, dtype=np.int8, order='c')
+    state = _max_len_seq_inner(taps, state, nbits, length, seq)
+    return seq, state

venv/Lib/site-packages/scipy/signal/_savitzky_golay.py

@@ -0,0 +1,351 @@
+import numpy as np
+from scipy.linalg import lstsq
+from math import factorial
+from scipy.ndimage import convolve1d
+from ._arraytools import axis_slice
+
+
+def savgol_coeffs(window_length, polyorder, deriv=0, delta=1.0, pos=None,
+                  use="conv"):
+    """Compute the coefficients for a 1-D Savitzky-Golay FIR filter.
+
+    Parameters
+    ----------
+    window_length : int
+        The length of the filter window (i.e., the number of coefficients).
+        `window_length` must be an odd positive integer.
+    polyorder : int
+        The order of the polynomial used to fit the samples.
+        `polyorder` must be less than `window_length`.
+    deriv : int, optional
+        The order of the derivative to compute. This must be a
+        nonnegative integer. The default is 0, which means to filter
+        the data without differentiating.
+    delta : float, optional
+        The spacing of the samples to which the filter will be applied.
+        This is only used if deriv > 0.
+    pos : int or None, optional
+        If pos is not None, it specifies evaluation position within the
+        window. The default is the middle of the window.
+    use : str, optional
+        Either 'conv' or 'dot'. This argument chooses the order of the
+        coefficients. The default is 'conv', which means that the
+        coefficients are ordered to be used in a convolution. With
+        use='dot', the order is reversed, so the filter is applied by
+        dotting the coefficients with the data set.
+
+    Returns
+    -------
+    coeffs : 1-D ndarray
+        The filter coefficients.
+
+    References
+    ----------
+    A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by
+    Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8),
+    pp 1627-1639.
+
+    See Also
+    --------
+    savgol_filter
+
+    Notes
+    -----
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.signal import savgol_coeffs
+    >>> savgol_coeffs(5, 2)
+    array([-0.08571429,  0.34285714,  0.48571429,  0.34285714, -0.08571429])
+    >>> savgol_coeffs(5, 2, deriv=1)
+    array([ 2.00000000e-01,  1.00000000e-01,  2.07548111e-16, -1.00000000e-01,
+           -2.00000000e-01])
+
+    Note that use='dot' simply reverses the coefficients.
+
+    >>> savgol_coeffs(5, 2, pos=3)
+    array([ 0.25714286,  0.37142857,  0.34285714,  0.17142857, -0.14285714])
+    >>> savgol_coeffs(5, 2, pos=3, use='dot')
+    array([-0.14285714,  0.17142857,  0.34285714,  0.37142857,  0.25714286])
+
+    `x` contains data from the parabola x = t**2, sampled at
+    t = -1, 0, 1, 2, 3.  `c` holds the coefficients that will compute the
+    derivative at the last position.  When dotted with `x` the result should
+    be 6.
+
+    >>> x = np.array([1, 0, 1, 4, 9])
+    >>> c = savgol_coeffs(5, 2, pos=4, deriv=1, use='dot')
+    >>> c.dot(x)
+    6.0
+    """
+
+    # An alternative method for finding the coefficients when deriv=0 is
+    #    t = np.arange(window_length)
+    #    unit = (t == pos).astype(int)
+    #    coeffs = np.polyval(np.polyfit(t, unit, polyorder), t)
+    # The method implemented here is faster.
+
+    # To recreate the table of sample coefficients shown in the chapter on
+    # the Savitzy-Golay filter in the Numerical Recipes book, use
+    #    window_length = nL + nR + 1
+    #    pos = nL + 1
+    #    c = savgol_coeffs(window_length, M, pos=pos, use='dot')
+
+    if polyorder >= window_length:
+        raise ValueError("polyorder must be less than window_length.")
+
+    halflen, rem = divmod(window_length, 2)
+
+    if rem == 0:
+        raise ValueError("window_length must be odd.")
+
+    if pos is None:
+        pos = halflen
+
+    if not (0 <= pos < window_length):
+        raise ValueError("pos must be nonnegative and less than "
+                         "window_length.")
+
+    if use not in ['conv', 'dot']:
+        raise ValueError("`use` must be 'conv' or 'dot'")
+
+    if deriv > polyorder:
+        coeffs = np.zeros(window_length)
+        return coeffs
+
+    # Form the design matrix A. The columns of A are powers of the integers
+    # from -pos to window_length - pos - 1. The powers (i.e., rows) range
+    # from 0 to polyorder. (That is, A is a vandermonde matrix, but not
+    # necessarily square.)
+    x = np.arange(-pos, window_length - pos, dtype=float)
+    if use == "conv":
+        # Reverse so that result can be used in a convolution.
+        x = x[::-1]
+
+    order = np.arange(polyorder + 1).reshape(-1, 1)
+    A = x ** order
+
+    # y determines which order derivative is returned.
+    y = np.zeros(polyorder + 1)
+    # The coefficient assigned to y[deriv] scales the result to take into
+    # account the order of the derivative and the sample spacing.
+    y[deriv] = factorial(deriv) / (delta ** deriv)
+
+    # Find the least-squares solution of A*c = y
+    coeffs, _, _, _ = lstsq(A, y)
+
+    return coeffs
+
+
+def _polyder(p, m):
+    """Differentiate polynomials represented with coefficients.
+
+    p must be a 1-D or 2-D array.  In the 2-D case, each column gives
+    the coefficients of a polynomial; the first row holds the coefficients
+    associated with the highest power. m must be a nonnegative integer.
+    (numpy.polyder doesn't handle the 2-D case.)
+    """
+
+    if m == 0:
+        result = p
+    else:
+        n = len(p)
+        if n <= m:
+            result = np.zeros_like(p[:1, ...])
+        else:
+            dp = p[:-m].copy()
+            for k in range(m):
+                rng = np.arange(n - k - 1, m - k - 1, -1)
+                dp *= rng.reshape((n - m,) + (1,) * (p.ndim - 1))
+            result = dp
+    return result
+
+
+def _fit_edge(x, window_start, window_stop, interp_start, interp_stop,
+              axis, polyorder, deriv, delta, y):
+    """
+    Given an N-d array `x` and the specification of a slice of `x` from
+    `window_start` to `window_stop` along `axis`, create an interpolating
+    polynomial of each 1-D slice, and evaluate that polynomial in the slice
+    from `interp_start` to `interp_stop`. Put the result into the
+    corresponding slice of `y`.
+    """
+
+    # Get the edge into a (window_length, -1) array.
+    x_edge = axis_slice(x, start=window_start, stop=window_stop, axis=axis)
+    if axis == 0 or axis == -x.ndim:
+        xx_edge = x_edge
+        swapped = False
+    else:
+        xx_edge = x_edge.swapaxes(axis, 0)
+        swapped = True
+    xx_edge = xx_edge.reshape(xx_edge.shape[0], -1)
+
+    # Fit the edges.  poly_coeffs has shape (polyorder + 1, -1),
+    # where '-1' is the same as in xx_edge.
+    poly_coeffs = np.polyfit(np.arange(0, window_stop - window_start),
+                             xx_edge, polyorder)
+
+    if deriv > 0:
+        poly_coeffs = _polyder(poly_coeffs, deriv)
+
+    # Compute the interpolated values for the edge.
+    i = np.arange(interp_start - window_start, interp_stop - window_start)
+    values = np.polyval(poly_coeffs, i.reshape(-1, 1)) / (delta ** deriv)
+
+    # Now put the values into the appropriate slice of y.
+    # First reshape values to match y.
+    shp = list(y.shape)
+    shp[0], shp[axis] = shp[axis], shp[0]
+    values = values.reshape(interp_stop - interp_start, *shp[1:])
+    if swapped:
+        values = values.swapaxes(0, axis)
+    # Get a view of the data to be replaced by values.
+    y_edge = axis_slice(y, start=interp_start, stop=interp_stop, axis=axis)
+    y_edge[...] = values
+
+
+def _fit_edges_polyfit(x, window_length, polyorder, deriv, delta, axis, y):
+    """
+    Use polynomial interpolation of x at the low and high ends of the axis
+    to fill in the halflen values in y.
+
+    This function just calls _fit_edge twice, once for each end of the axis.
+    """
+    halflen = window_length // 2
+    _fit_edge(x, 0, window_length, 0, halflen, axis,
+              polyorder, deriv, delta, y)
+    n = x.shape[axis]
+    _fit_edge(x, n - window_length, n, n - halflen, n, axis,
+              polyorder, deriv, delta, y)
+
+
+def savgol_filter(x, window_length, polyorder, deriv=0, delta=1.0,
+                  axis=-1, mode='interp', cval=0.0):
+    """ Apply a Savitzky-Golay filter to an array.
+
+    This is a 1-D filter. If `x`  has dimension greater than 1, `axis`
+    determines the axis along which the filter is applied.
+
+    Parameters
+    ----------
+    x : array_like
+        The data to be filtered. If `x` is not a single or double precision
+        floating point array, it will be converted to type ``numpy.float64``
+        before filtering.
+    window_length : int
+        The length of the filter window (i.e., the number of coefficients).
+        `window_length` must be a positive odd integer. If `mode` is 'interp',
+        `window_length` must be less than or equal to the size of `x`.
+    polyorder : int
+        The order of the polynomial used to fit the samples.
+        `polyorder` must be less than `window_length`.
+    deriv : int, optional
+        The order of the derivative to compute. This must be a
+        nonnegative integer. The default is 0, which means to filter
+        the data without differentiating.
+    delta : float, optional
+        The spacing of the samples to which the filter will be applied.
+        This is only used if deriv > 0. Default is 1.0.
+    axis : int, optional
+        The axis of the array `x` along which the filter is to be applied.
+        Default is -1.
+    mode : str, optional
+        Must be 'mirror', 'constant', 'nearest', 'wrap' or 'interp'. This
+        determines the type of extension to use for the padded signal to
+        which the filter is applied.  When `mode` is 'constant', the padding
+        value is given by `cval`.  See the Notes for more details on 'mirror',
+        'constant', 'wrap', and 'nearest'.
+        When the 'interp' mode is selected (the default), no extension
+        is used.  Instead, a degree `polyorder` polynomial is fit to the
+        last `window_length` values of the edges, and this polynomial is
+        used to evaluate the last `window_length // 2` output values.
+    cval : scalar, optional
+        Value to fill past the edges of the input if `mode` is 'constant'.
+        Default is 0.0.
+
+    Returns
+    -------
+    y : ndarray, same shape as `x`
+        The filtered data.
+
+    See Also
+    --------
+    savgol_coeffs
+
+    Notes
+    -----
+    Details on the `mode` options:
+
+        'mirror':
+            Repeats the values at the edges in reverse order. The value
+            closest to the edge is not included.
+        'nearest':
+            The extension contains the nearest input value.
+        'constant':
+            The extension contains the value given by the `cval` argument.
+        'wrap':
+            The extension contains the values from the other end of the array.
+
+    For example, if the input is [1, 2, 3, 4, 5, 6, 7, 8], and
+    `window_length` is 7, the following shows the extended data for
+    the various `mode` options (assuming `cval` is 0)::
+
+        mode       |   Ext   |         Input          |   Ext
+        -----------+---------+------------------------+---------
+        'mirror'   | 4  3  2 | 1  2  3  4  5  6  7  8 | 7  6  5
+        'nearest'  | 1  1  1 | 1  2  3  4  5  6  7  8 | 8  8  8
+        'constant' | 0  0  0 | 1  2  3  4  5  6  7  8 | 0  0  0
+        'wrap'     | 6  7  8 | 1  2  3  4  5  6  7  8 | 1  2  3
+
+    .. versionadded:: 0.14.0
+
+    Examples
+    --------
+    >>> from scipy.signal import savgol_filter
+    >>> np.set_printoptions(precision=2)  # For compact display.
+    >>> x = np.array([2, 2, 5, 2, 1, 0, 1, 4, 9])
+
+    Filter with a window length of 5 and a degree 2 polynomial.  Use
+    the defaults for all other parameters.
+
+    >>> savgol_filter(x, 5, 2)
+    array([1.66, 3.17, 3.54, 2.86, 0.66, 0.17, 1.  , 4.  , 9.  ])
+
+    Note that the last five values in x are samples of a parabola, so
+    when mode='interp' (the default) is used with polyorder=2, the last
+    three values are unchanged. Compare that to, for example,
+    `mode='nearest'`:
+
+    >>> savgol_filter(x, 5, 2, mode='nearest')
+    array([1.74, 3.03, 3.54, 2.86, 0.66, 0.17, 1.  , 4.6 , 7.97])
+
+    """
+    if mode not in ["mirror", "constant", "nearest", "interp", "wrap"]:
+        raise ValueError("mode must be 'mirror', 'constant', 'nearest' "
+                         "'wrap' or 'interp'.")
+
+    x = np.asarray(x)
+    # Ensure that x is either single or double precision floating point.
+    if x.dtype != np.float64 and x.dtype != np.float32:
+        x = x.astype(np.float64)
+
+    coeffs = savgol_coeffs(window_length, polyorder, deriv=deriv, delta=delta)
+
+    if mode == "interp":
+        if window_length > x.size:
+            raise ValueError("If mode is 'interp', window_length must be less "
+                             "than or equal to the size of x.")
+
+        # Do not pad. Instead, for the elements within `window_length // 2`
+        # of the ends of the sequence, use the polynomial that is fitted to
+        # the last `window_length` elements.
+        y = convolve1d(x, coeffs, axis=axis, mode="constant")
+        _fit_edges_polyfit(x, window_length, polyorder, deriv, delta, axis, y)
+    else:
+        # Any mode other than 'interp' is passed on to ndimage.convolve1d.
+        y = convolve1d(x, coeffs, axis=axis, mode=mode, cval=cval)
+
+    return y

venv/Lib/site-packages/scipy/signal/_upfirdn.py

@@ -0,0 +1,215 @@
+# Code adapted from "upfirdn" python library with permission:
+#
+# Copyright (c) 2009, Motorola, Inc
+#
+# All Rights Reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are
+# met:
+#
+# * Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# * Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# * Neither the name of Motorola nor the names of its contributors may be
+# used to endorse or promote products derived from this software without
+# specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+import numpy as np
+
+from ._upfirdn_apply import _output_len, _apply, mode_enum
+
+__all__ = ['upfirdn', '_output_len']
+
+_upfirdn_modes = [
+    'constant', 'wrap', 'edge', 'smooth', 'symmetric', 'reflect',
+    'antisymmetric', 'antireflect', 'line',
+]
+
+
+def _pad_h(h, up):
+    """Store coefficients in a transposed, flipped arrangement.
+
+    For example, suppose upRate is 3, and the
+    input number of coefficients is 10, represented as h[0], ..., h[9].
+
+    Then the internal buffer will look like this::
+
+       h[9], h[6], h[3], h[0],   // flipped phase 0 coefs
+       0,    h[7], h[4], h[1],   // flipped phase 1 coefs (zero-padded)
+       0,    h[8], h[5], h[2],   // flipped phase 2 coefs (zero-padded)
+
+    """
+    h_padlen = len(h) + (-len(h) % up)
+    h_full = np.zeros(h_padlen, h.dtype)
+    h_full[:len(h)] = h
+    h_full = h_full.reshape(-1, up).T[:, ::-1].ravel()
+    return h_full
+
+
+def _check_mode(mode):
+    mode = mode.lower()
+    enum = mode_enum(mode)
+    return enum
+
+
+class _UpFIRDn(object):
+    """Helper for resampling."""
+
+    def __init__(self, h, x_dtype, up, down):
+        h = np.asarray(h)
+        if h.ndim != 1 or h.size == 0:
+            raise ValueError('h must be 1-D with non-zero length')
+        self._output_type = np.result_type(h.dtype, x_dtype, np.float32)
+        h = np.asarray(h, self._output_type)
+        self._up = int(up)
+        self._down = int(down)
+        if self._up < 1 or self._down < 1:
+            raise ValueError('Both up and down must be >= 1')
+        # This both transposes, and "flips" each phase for filtering
+        self._h_trans_flip = _pad_h(h, self._up)
+        self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip)
+        self._h_len_orig = len(h)
+
+    def apply_filter(self, x, axis=-1, mode='constant', cval=0):
+        """Apply the prepared filter to the specified axis of N-D signal x."""
+        output_len = _output_len(self._h_len_orig, x.shape[axis],
+                                 self._up, self._down)
+        # Explicit use of np.int64 for output_shape dtype avoids OverflowError
+        # when allocating large array on platforms where np.int_ is 32 bits
+        output_shape = np.asarray(x.shape, dtype=np.int64)
+        output_shape[axis] = output_len
+        out = np.zeros(output_shape, dtype=self._output_type, order='C')
+        axis = axis % x.ndim
+        mode = _check_mode(mode)
+        _apply(np.asarray(x, self._output_type),
+               self._h_trans_flip, out,
+               self._up, self._down, axis, mode, cval)
+        return out
+
+
+def upfirdn(h, x, up=1, down=1, axis=-1, mode='constant', cval=0):
+    """Upsample, FIR filter, and downsample.
+
+    Parameters
+    ----------
+    h : array_like
+        1-D FIR (finite-impulse response) filter coefficients.
+    x : array_like
+        Input signal array.
+    up : int, optional
+        Upsampling rate. Default is 1.
+    down : int, optional
+        Downsampling rate. Default is 1.
+    axis : int, optional
+        The axis of the input data array along which to apply the
+        linear filter. The filter is applied to each subarray along
+        this axis. Default is -1.
+    mode : str, optional
+        The signal extension mode to use. The set
+        ``{"constant", "symmetric", "reflect", "edge", "wrap"}`` correspond to
+        modes provided by `numpy.pad`. ``"smooth"`` implements a smooth
+        extension by extending based on the slope of the last 2 points at each
+        end of the array. ``"antireflect"`` and ``"antisymmetric"`` are
+        anti-symmetric versions of ``"reflect"`` and ``"symmetric"``. The mode
+        `"line"` extends the signal based on a linear trend defined by the
+        first and last points along the ``axis``.
+
+        .. versionadded:: 1.4.0
+    cval : float, optional
+        The constant value to use when ``mode == "constant"``.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    y : ndarray
+        The output signal array. Dimensions will be the same as `x` except
+        for along `axis`, which will change size according to the `h`,
+        `up`,  and `down` parameters.
+
+    Notes
+    -----
+    The algorithm is an implementation of the block diagram shown on page 129
+    of the Vaidyanathan text [1]_ (Figure 4.3-8d).
+
+    The direct approach of upsampling by factor of P with zero insertion,
+    FIR filtering of length ``N``, and downsampling by factor of Q is
+    O(N*Q) per output sample. The polyphase implementation used here is
+    O(N/P).
+
+    .. versionadded:: 0.18
+
+    References
+    ----------
+    .. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks,
+           Prentice Hall, 1993.
+
+    Examples
+    --------
+    Simple operations:
+
+    >>> from scipy.signal import upfirdn
+    >>> upfirdn([1, 1, 1], [1, 1, 1])   # FIR filter
+    array([ 1.,  2.,  3.,  2.,  1.])
+    >>> upfirdn([1], [1, 2, 3], 3)  # upsampling with zeros insertion
+    array([ 1.,  0.,  0.,  2.,  0.,  0.,  3.,  0.,  0.])
+    >>> upfirdn([1, 1, 1], [1, 2, 3], 3)  # upsampling with sample-and-hold
+    array([ 1.,  1.,  1.,  2.,  2.,  2.,  3.,  3.,  3.])
+    >>> upfirdn([.5, 1, .5], [1, 1, 1], 2)  # linear interpolation
+    array([ 0.5,  1. ,  1. ,  1. ,  1. ,  1. ,  0.5,  0. ])
+    >>> upfirdn([1], np.arange(10), 1, 3)  # decimation by 3
+    array([ 0.,  3.,  6.,  9.])
+    >>> upfirdn([.5, 1, .5], np.arange(10), 2, 3)  # linear interp, rate 2/3
+    array([ 0. ,  1. ,  2.5,  4. ,  5.5,  7. ,  8.5,  0. ])
+
+    Apply a single filter to multiple signals:
+
+    >>> x = np.reshape(np.arange(8), (4, 2))
+    >>> x
+    array([[0, 1],
+           [2, 3],
+           [4, 5],
+           [6, 7]])
+
+    Apply along the last dimension of ``x``:
+
+    >>> h = [1, 1]
+    >>> upfirdn(h, x, 2)
+    array([[ 0.,  0.,  1.,  1.],
+           [ 2.,  2.,  3.,  3.],
+           [ 4.,  4.,  5.,  5.],
+           [ 6.,  6.,  7.,  7.]])
+
+    Apply along the 0th dimension of ``x``:
+
+    >>> upfirdn(h, x, 2, axis=0)
+    array([[ 0.,  1.],
+           [ 0.,  1.],
+           [ 2.,  3.],
+           [ 2.,  3.],
+           [ 4.,  5.],
+           [ 4.,  5.],
+           [ 6.,  7.],
+           [ 6.,  7.]])
+    """
+    x = np.asarray(x)
+    ufd = _UpFIRDn(h, x.dtype, up, down)
+    # This is equivalent to (but faster than) using np.apply_along_axis
+    return ufd.apply_filter(x, axis, mode, cval)

venv/Lib/site-packages/scipy/signal/bsplines.py

@@ -0,0 +1,451 @@
+from numpy import (logical_and, asarray, pi, zeros_like,
+                   piecewise, array, arctan2, tan, zeros, arange, floor)
+from numpy.core.umath import (sqrt, exp, greater, less, cos, add, sin,
+                              less_equal, greater_equal)
+
+# From splinemodule.c
+from .spline import cspline2d, sepfir2d
+
+from scipy.special import comb, gamma
+
+__all__ = ['spline_filter', 'bspline', 'gauss_spline', 'cubic', 'quadratic',
+           'cspline1d', 'qspline1d', 'cspline1d_eval', 'qspline1d_eval']
+
+
+def factorial(n):
+    return gamma(n + 1)
+
+
+def spline_filter(Iin, lmbda=5.0):
+    """Smoothing spline (cubic) filtering of a rank-2 array.
+
+    Filter an input data set, `Iin`, using a (cubic) smoothing spline of
+    fall-off `lmbda`.
+    """
+    intype = Iin.dtype.char
+    hcol = array([1.0, 4.0, 1.0], 'f') / 6.0
+    if intype in ['F', 'D']:
+        Iin = Iin.astype('F')
+        ckr = cspline2d(Iin.real, lmbda)
+        cki = cspline2d(Iin.imag, lmbda)
+        outr = sepfir2d(ckr, hcol, hcol)
+        outi = sepfir2d(cki, hcol, hcol)
+        out = (outr + 1j * outi).astype(intype)
+    elif intype in ['f', 'd']:
+        ckr = cspline2d(Iin, lmbda)
+        out = sepfir2d(ckr, hcol, hcol)
+        out = out.astype(intype)
+    else:
+        raise TypeError("Invalid data type for Iin")
+    return out
+
+
+_splinefunc_cache = {}
+
+
+def _bspline_piecefunctions(order):
+    """Returns the function defined over the left-side pieces for a bspline of
+    a given order.
+
+    The 0th piece is the first one less than 0. The last piece is a function
+    identical to 0 (returned as the constant 0). (There are order//2 + 2 total
+    pieces).
+
+    Also returns the condition functions that when evaluated return boolean
+    arrays for use with `numpy.piecewise`.
+    """
+    try:
+        return _splinefunc_cache[order]
+    except KeyError:
+        pass
+
+    def condfuncgen(num, val1, val2):
+        if num == 0:
+            return lambda x: logical_and(less_equal(x, val1),
+                                         greater_equal(x, val2))
+        elif num == 2:
+            return lambda x: less_equal(x, val2)
+        else:
+            return lambda x: logical_and(less(x, val1),
+                                         greater_equal(x, val2))
+
+    last = order // 2 + 2
+    if order % 2:
+        startbound = -1.0
+    else:
+        startbound = -0.5
+    condfuncs = [condfuncgen(0, 0, startbound)]
+    bound = startbound
+    for num in range(1, last - 1):
+        condfuncs.append(condfuncgen(1, bound, bound - 1))
+        bound = bound - 1
+    condfuncs.append(condfuncgen(2, 0, -(order + 1) / 2.0))
+
+    # final value of bound is used in piecefuncgen below
+
+    # the functions to evaluate are taken from the left-hand side
+    #  in the general expression derived from the central difference
+    #  operator (because they involve fewer terms).
+
+    fval = factorial(order)
+
+    def piecefuncgen(num):
+        Mk = order // 2 - num
+        if (Mk < 0):
+            return 0  # final function is 0
+        coeffs = [(1 - 2 * (k % 2)) * float(comb(order + 1, k, exact=1)) / fval
+                  for k in range(Mk + 1)]
+        shifts = [-bound - k for k in range(Mk + 1)]
+
+        def thefunc(x):
+            res = 0.0
+            for k in range(Mk + 1):
+                res += coeffs[k] * (x + shifts[k]) ** order
+            return res
+        return thefunc
+
+    funclist = [piecefuncgen(k) for k in range(last)]
+
+    _splinefunc_cache[order] = (funclist, condfuncs)
+
+    return funclist, condfuncs
+
+
+def bspline(x, n):
+    """B-spline basis function of order n.
+
+    Notes
+    -----
+    Uses numpy.piecewise and automatic function-generator.
+
+    """
+    ax = -abs(asarray(x))
+    # number of pieces on the left-side is (n+1)/2
+    funclist, condfuncs = _bspline_piecefunctions(n)
+    condlist = [func(ax) for func in condfuncs]
+    return piecewise(ax, condlist, funclist)
+
+
+def gauss_spline(x, n):
+    """Gaussian approximation to B-spline basis function of order n.
+
+    Parameters
+    ----------
+    n : int
+        The order of the spline. Must be nonnegative, i.e., n >= 0
+
+    References
+    ----------
+    .. [1] Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen
+       F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In:
+       Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational
+       Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer
+       Science, vol 4485. Springer, Berlin, Heidelberg
+   """
+    signsq = (n + 1) / 12.0
+    return 1 / sqrt(2 * pi * signsq) * exp(-x ** 2 / 2 / signsq)
+
+
+def cubic(x):
+    """A cubic B-spline.
+
+    This is a special case of `bspline`, and equivalent to ``bspline(x, 3)``.
+    """
+    ax = abs(asarray(x))
+    res = zeros_like(ax)
+    cond1 = less(ax, 1)
+    if cond1.any():
+        ax1 = ax[cond1]
+        res[cond1] = 2.0 / 3 - 1.0 / 2 * ax1 ** 2 * (2 - ax1)
+    cond2 = ~cond1 & less(ax, 2)
+    if cond2.any():
+        ax2 = ax[cond2]
+        res[cond2] = 1.0 / 6 * (2 - ax2) ** 3
+    return res
+
+
+def quadratic(x):
+    """A quadratic B-spline.
+
+    This is a special case of `bspline`, and equivalent to ``bspline(x, 2)``.
+    """
+    ax = abs(asarray(x))
+    res = zeros_like(ax)
+    cond1 = less(ax, 0.5)
+    if cond1.any():
+        ax1 = ax[cond1]
+        res[cond1] = 0.75 - ax1 ** 2
+    cond2 = ~cond1 & less(ax, 1.5)
+    if cond2.any():
+        ax2 = ax[cond2]
+        res[cond2] = (ax2 - 1.5) ** 2 / 2.0
+    return res
+
+
+def _coeff_smooth(lam):
+    xi = 1 - 96 * lam + 24 * lam * sqrt(3 + 144 * lam)
+    omeg = arctan2(sqrt(144 * lam - 1), sqrt(xi))
+    rho = (24 * lam - 1 - sqrt(xi)) / (24 * lam)
+    rho = rho * sqrt((48 * lam + 24 * lam * sqrt(3 + 144 * lam)) / xi)
+    return rho, omeg
+
+
+def _hc(k, cs, rho, omega):
+    return (cs / sin(omega) * (rho ** k) * sin(omega * (k + 1)) *
+            greater(k, -1))
+
+
+def _hs(k, cs, rho, omega):
+    c0 = (cs * cs * (1 + rho * rho) / (1 - rho * rho) /
+          (1 - 2 * rho * rho * cos(2 * omega) + rho ** 4))
+    gamma = (1 - rho * rho) / (1 + rho * rho) / tan(omega)
+    ak = abs(k)
+    return c0 * rho ** ak * (cos(omega * ak) + gamma * sin(omega * ak))
+
+
+def _cubic_smooth_coeff(signal, lamb):
+    rho, omega = _coeff_smooth(lamb)
+    cs = 1 - 2 * rho * cos(omega) + rho * rho
+    K = len(signal)
+    yp = zeros((K,), signal.dtype.char)
+    k = arange(K)
+    yp[0] = (_hc(0, cs, rho, omega) * signal[0] +
+             add.reduce(_hc(k + 1, cs, rho, omega) * signal))
+
+    yp[1] = (_hc(0, cs, rho, omega) * signal[0] +
+             _hc(1, cs, rho, omega) * signal[1] +
+             add.reduce(_hc(k + 2, cs, rho, omega) * signal))
+
+    for n in range(2, K):
+        yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] -
+                 rho * rho * yp[n - 2])
+
+    y = zeros((K,), signal.dtype.char)
+
+    y[K - 1] = add.reduce((_hs(k, cs, rho, omega) +
+                           _hs(k + 1, cs, rho, omega)) * signal[::-1])
+    y[K - 2] = add.reduce((_hs(k - 1, cs, rho, omega) +
+                           _hs(k + 2, cs, rho, omega)) * signal[::-1])
+
+    for n in range(K - 3, -1, -1):
+        y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] -
+                rho * rho * y[n + 2])
+
+    return y
+
+
+def _cubic_coeff(signal):
+    zi = -2 + sqrt(3)
+    K = len(signal)
+    yplus = zeros((K,), signal.dtype.char)
+    powers = zi ** arange(K)
+    yplus[0] = signal[0] + zi * add.reduce(powers * signal)
+    for k in range(1, K):
+        yplus[k] = signal[k] + zi * yplus[k - 1]
+    output = zeros((K,), signal.dtype)
+    output[K - 1] = zi / (zi - 1) * yplus[K - 1]
+    for k in range(K - 2, -1, -1):
+        output[k] = zi * (output[k + 1] - yplus[k])
+    return output * 6.0
+
+
+def _quadratic_coeff(signal):
+    zi = -3 + 2 * sqrt(2.0)
+    K = len(signal)
+    yplus = zeros((K,), signal.dtype.char)
+    powers = zi ** arange(K)
+    yplus[0] = signal[0] + zi * add.reduce(powers * signal)
+    for k in range(1, K):
+        yplus[k] = signal[k] + zi * yplus[k - 1]
+    output = zeros((K,), signal.dtype.char)
+    output[K - 1] = zi / (zi - 1) * yplus[K - 1]
+    for k in range(K - 2, -1, -1):
+        output[k] = zi * (output[k + 1] - yplus[k])
+    return output * 8.0
+
+
+def cspline1d(signal, lamb=0.0):
+    """
+    Compute cubic spline coefficients for rank-1 array.
+
+    Find the cubic spline coefficients for a 1-D signal assuming
+    mirror-symmetric boundary conditions. To obtain the signal back from the
+    spline representation mirror-symmetric-convolve these coefficients with a
+    length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 .
+
+    Parameters
+    ----------
+    signal : ndarray
+        A rank-1 array representing samples of a signal.
+    lamb : float, optional
+        Smoothing coefficient, default is 0.0.
+
+    Returns
+    -------
+    c : ndarray
+        Cubic spline coefficients.
+
+    """
+    if lamb != 0.0:
+        return _cubic_smooth_coeff(signal, lamb)
+    else:
+        return _cubic_coeff(signal)
+
+
+def qspline1d(signal, lamb=0.0):
+    """Compute quadratic spline coefficients for rank-1 array.
+
+    Parameters
+    ----------
+    signal : ndarray
+        A rank-1 array representing samples of a signal.
+    lamb : float, optional
+        Smoothing coefficient (must be zero for now).
+
+    Returns
+    -------
+    c : ndarray
+        Quadratic spline coefficients.
+
+    See Also
+    --------
+    qspline1d_eval : Evaluate a quadratic spline at the new set of points.
+
+    Notes
+    -----
+    Find the quadratic spline coefficients for a 1-D signal assuming
+    mirror-symmetric boundary conditions. To obtain the signal back from the
+    spline representation mirror-symmetric-convolve these coefficients with a
+    length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 .
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a quadratic spline:
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import qspline1d, qspline1d_eval
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += np.random.randn(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = qspline1d_eval(qspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    if lamb != 0.0:
+        raise ValueError("Smoothing quadratic splines not supported yet.")
+    else:
+        return _quadratic_coeff(signal)
+
+
+def cspline1d_eval(cj, newx, dx=1.0, x0=0):
+    """Evaluate a spline at the new set of points.
+
+    `dx` is the old sample-spacing while `x0` was the old origin. In
+    other-words the old-sample points (knot-points) for which the `cj`
+    represent spline coefficients were at equally-spaced points of:
+
+      oldx = x0 + j*dx  j=0...N-1, with N=len(cj)
+
+    Edges are handled using mirror-symmetric boundary conditions.
+
+    """
+    newx = (asarray(newx) - x0) / float(dx)
+    res = zeros_like(newx, dtype=cj.dtype)
+    if res.size == 0:
+        return res
+    N = len(cj)
+    cond1 = newx < 0
+    cond2 = newx > (N - 1)
+    cond3 = ~(cond1 | cond2)
+    # handle general mirror-symmetry
+    res[cond1] = cspline1d_eval(cj, -newx[cond1])
+    res[cond2] = cspline1d_eval(cj, 2 * (N - 1) - newx[cond2])
+    newx = newx[cond3]
+    if newx.size == 0:
+        return res
+    result = zeros_like(newx, dtype=cj.dtype)
+    jlower = floor(newx - 2).astype(int) + 1
+    for i in range(4):
+        thisj = jlower + i
+        indj = thisj.clip(0, N - 1)  # handle edge cases
+        result += cj[indj] * cubic(newx - thisj)
+    res[cond3] = result
+    return res
+
+
+def qspline1d_eval(cj, newx, dx=1.0, x0=0):
+    """Evaluate a quadratic spline at the new set of points.
+
+    Parameters
+    ----------
+    cj : ndarray
+        Quadratic spline coefficients
+    newx : ndarray
+        New set of points.
+    dx : float, optional
+        Old sample-spacing, the default value is 1.0.
+    x0 : int, optional
+        Old origin, the default value is 0.
+
+    Returns
+    -------
+    res : ndarray
+        Evaluated a quadratic spline points.
+
+    See Also
+    --------
+    qspline1d : Compute quadratic spline coefficients for rank-1 array.
+
+    Notes
+    -----
+    `dx` is the old sample-spacing while `x0` was the old origin. In
+    other-words the old-sample points (knot-points) for which the `cj`
+    represent spline coefficients were at equally-spaced points of::
+
+      oldx = x0 + j*dx  j=0...N-1, with N=len(cj)
+
+    Edges are handled using mirror-symmetric boundary conditions.
+
+    Examples
+    --------
+    We can filter a signal to reduce and smooth out high-frequency noise with
+    a quadratic spline:
+
+    >>> import matplotlib.pyplot as plt
+    >>> from scipy.signal import qspline1d, qspline1d_eval
+    >>> sig = np.repeat([0., 1., 0.], 100)
+    >>> sig += np.random.randn(len(sig))*0.05  # add noise
+    >>> time = np.linspace(0, len(sig))
+    >>> filtered = qspline1d_eval(qspline1d(sig), time)
+    >>> plt.plot(sig, label="signal")
+    >>> plt.plot(time, filtered, label="filtered")
+    >>> plt.legend()
+    >>> plt.show()
+
+    """
+    newx = (asarray(newx) - x0) / dx
+    res = zeros_like(newx)
+    if res.size == 0:
+        return res
+    N = len(cj)
+    cond1 = newx < 0
+    cond2 = newx > (N - 1)
+    cond3 = ~(cond1 | cond2)
+    # handle general mirror-symmetry
+    res[cond1] = qspline1d_eval(cj, -newx[cond1])
+    res[cond2] = qspline1d_eval(cj, 2 * (N - 1) - newx[cond2])
+    newx = newx[cond3]
+    if newx.size == 0:
+        return res
+    result = zeros_like(newx)
+    jlower = floor(newx - 1.5).astype(int) + 1
+    for i in range(3):
+        thisj = jlower + i
+        indj = thisj.clip(0, N - 1)  # handle edge cases
+        result += cj[indj] * quadratic(newx - thisj)
+    res[cond3] = result
+    return res

venv/Lib/site-packages/scipy/signal/lti_conversion.py

@@ -0,0 +1,502 @@
+"""
+ltisys -- a collection of functions to convert linear time invariant systems
+from one representation to another.
+"""
+import numpy
+import numpy as np
+from numpy import (r_, eye, atleast_2d, poly, dot,
+                   asarray, prod, zeros, array, outer)
+from scipy import linalg
+
+from .filter_design import tf2zpk, zpk2tf, normalize
+
+
+__all__ = ['tf2ss', 'abcd_normalize', 'ss2tf', 'zpk2ss', 'ss2zpk',
+           'cont2discrete']
+
+
+def tf2ss(num, den):
+    r"""Transfer function to state-space representation.
+
+    Parameters
+    ----------
+    num, den : array_like
+        Sequences representing the coefficients of the numerator and
+        denominator polynomials, in order of descending degree. The
+        denominator needs to be at least as long as the numerator.
+
+    Returns
+    -------
+    A, B, C, D : ndarray
+        State space representation of the system, in controller canonical
+        form.
+
+    Examples
+    --------
+    Convert the transfer function:
+
+    .. math:: H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}
+
+    >>> num = [1, 3, 3]
+    >>> den = [1, 2, 1]
+
+    to the state-space representation:
+
+    .. math::
+
+        \dot{\textbf{x}}(t) =
+        \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\
+
+        \textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)
+
+    >>> from scipy.signal import tf2ss
+    >>> A, B, C, D = tf2ss(num, den)
+    >>> A
+    array([[-2., -1.],
+           [ 1.,  0.]])
+    >>> B
+    array([[ 1.],
+           [ 0.]])
+    >>> C
+    array([[ 1.,  2.]])
+    >>> D
+    array([[ 1.]])
+    """
+    # Controller canonical state-space representation.
+    #  if M+1 = len(num) and K+1 = len(den) then we must have M <= K
+    #  states are found by asserting that X(s) = U(s) / D(s)
+    #  then Y(s) = N(s) * X(s)
+    #
+    #   A, B, C, and D follow quite naturally.
+    #
+    num, den = normalize(num, den)   # Strips zeros, checks arrays
+    nn = len(num.shape)
+    if nn == 1:
+        num = asarray([num], num.dtype)
+    M = num.shape[1]
+    K = len(den)
+    if M > K:
+        msg = "Improper transfer function. `num` is longer than `den`."
+        raise ValueError(msg)
+    if M == 0 or K == 0:  # Null system
+        return (array([], float), array([], float), array([], float),
+                array([], float))
+
+    # pad numerator to have same number of columns has denominator
+    num = r_['-1', zeros((num.shape[0], K - M), num.dtype), num]
+
+    if num.shape[-1] > 0:
+        D = atleast_2d(num[:, 0])
+
+    else:
+        # We don't assign it an empty array because this system
+        # is not 'null'. It just doesn't have a non-zero D
+        # matrix. Thus, it should have a non-zero shape so that
+        # it can be operated on by functions like 'ss2tf'
+        D = array([[0]], float)
+
+    if K == 1:
+        D = D.reshape(num.shape)
+
+        return (zeros((1, 1)), zeros((1, D.shape[1])),
+                zeros((D.shape[0], 1)), D)
+
+    frow = -array([den[1:]])
+    A = r_[frow, eye(K - 2, K - 1)]
+    B = eye(K - 1, 1)
+    C = num[:, 1:] - outer(num[:, 0], den[1:])
+    D = D.reshape((C.shape[0], B.shape[1]))
+
+    return A, B, C, D
+
+
+def _none_to_empty_2d(arg):
+    if arg is None:
+        return zeros((0, 0))
+    else:
+        return arg
+
+
+def _atleast_2d_or_none(arg):
+    if arg is not None:
+        return atleast_2d(arg)
+
+
+def _shape_or_none(M):
+    if M is not None:
+        return M.shape
+    else:
+        return (None,) * 2
+
+
+def _choice_not_none(*args):
+    for arg in args:
+        if arg is not None:
+            return arg
+
+
+def _restore(M, shape):
+    if M.shape == (0, 0):
+        return zeros(shape)
+    else:
+        if M.shape != shape:
+            raise ValueError("The input arrays have incompatible shapes.")
+        return M
+
+
+def abcd_normalize(A=None, B=None, C=None, D=None):
+    """Check state-space matrices and ensure they are 2-D.
+
+    If enough information on the system is provided, that is, enough
+    properly-shaped arrays are passed to the function, the missing ones
+    are built from this information, ensuring the correct number of
+    rows and columns. Otherwise a ValueError is raised.
+
+    Parameters
+    ----------
+    A, B, C, D : array_like, optional
+        State-space matrices. All of them are None (missing) by default.
+        See `ss2tf` for format.
+
+    Returns
+    -------
+    A, B, C, D : array
+        Properly shaped state-space matrices.
+
+    Raises
+    ------
+    ValueError
+        If not enough information on the system was provided.
+
+    """
+    A, B, C, D = map(_atleast_2d_or_none, (A, B, C, D))
+
+    MA, NA = _shape_or_none(A)
+    MB, NB = _shape_or_none(B)
+    MC, NC = _shape_or_none(C)
+    MD, ND = _shape_or_none(D)
+
+    p = _choice_not_none(MA, MB, NC)
+    q = _choice_not_none(NB, ND)
+    r = _choice_not_none(MC, MD)
+    if p is None or q is None or r is None:
+        raise ValueError("Not enough information on the system.")
+
+    A, B, C, D = map(_none_to_empty_2d, (A, B, C, D))
+    A = _restore(A, (p, p))
+    B = _restore(B, (p, q))
+    C = _restore(C, (r, p))
+    D = _restore(D, (r, q))
+
+    return A, B, C, D
+
+
+def ss2tf(A, B, C, D, input=0):
+    r"""State-space to transfer function.
+
+    A, B, C, D defines a linear state-space system with `p` inputs,
+    `q` outputs, and `n` state variables.
+
+    Parameters
+    ----------
+    A : array_like
+        State (or system) matrix of shape ``(n, n)``
+    B : array_like
+        Input matrix of shape ``(n, p)``
+    C : array_like
+        Output matrix of shape ``(q, n)``
+    D : array_like
+        Feedthrough (or feedforward) matrix of shape ``(q, p)``
+    input : int, optional
+        For multiple-input systems, the index of the input to use.
+
+    Returns
+    -------
+    num : 2-D ndarray
+        Numerator(s) of the resulting transfer function(s). `num` has one row
+        for each of the system's outputs. Each row is a sequence representation
+        of the numerator polynomial.
+    den : 1-D ndarray
+        Denominator of the resulting transfer function(s). `den` is a sequence
+        representation of the denominator polynomial.
+
+    Examples
+    --------
+    Convert the state-space representation:
+
+    .. math::
+
+        \dot{\textbf{x}}(t) =
+        \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\
+
+        \textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) +
+        \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)
+
+    >>> A = [[-2, -1], [1, 0]]
+    >>> B = [[1], [0]]  # 2-D column vector
+    >>> C = [[1, 2]]    # 2-D row vector
+    >>> D = 1
+
+    to the transfer function:
+
+    .. math:: H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}
+
+    >>> from scipy.signal import ss2tf
+    >>> ss2tf(A, B, C, D)
+    (array([[1, 3, 3]]), array([ 1.,  2.,  1.]))
+    """
+    # transfer function is C (sI - A)**(-1) B + D
+
+    # Check consistency and make them all rank-2 arrays
+    A, B, C, D = abcd_normalize(A, B, C, D)
+
+    nout, nin = D.shape
+    if input >= nin:
+        raise ValueError("System does not have the input specified.")
+
+    # make SIMO from possibly MIMO system.
+    B = B[:, input:input + 1]
+    D = D[:, input:input + 1]
+
+    try:
+        den = poly(A)
+    except ValueError:
+        den = 1
+
+    if (prod(B.shape, axis=0) == 0) and (prod(C.shape, axis=0) == 0):
+        num = numpy.ravel(D)
+        if (prod(D.shape, axis=0) == 0) and (prod(A.shape, axis=0) == 0):
+            den = []
+        return num, den
+
+    num_states = A.shape[0]
+    type_test = A[:, 0] + B[:, 0] + C[0, :] + D
+    num = numpy.zeros((nout, num_states + 1), type_test.dtype)
+    for k in range(nout):
+        Ck = atleast_2d(C[k, :])
+        num[k] = poly(A - dot(B, Ck)) + (D[k] - 1) * den
+
+    return num, den
+
+
+def zpk2ss(z, p, k):
+    """Zero-pole-gain representation to state-space representation
+
+    Parameters
+    ----------
+    z, p : sequence
+        Zeros and poles.
+    k : float
+        System gain.
+
+    Returns
+    -------
+    A, B, C, D : ndarray
+        State space representation of the system, in controller canonical
+        form.
+
+    """
+    return tf2ss(*zpk2tf(z, p, k))
+
+
+def ss2zpk(A, B, C, D, input=0):
+    """State-space representation to zero-pole-gain representation.
+
+    A, B, C, D defines a linear state-space system with `p` inputs,
+    `q` outputs, and `n` state variables.
+
+    Parameters
+    ----------
+    A : array_like
+        State (or system) matrix of shape ``(n, n)``
+    B : array_like
+        Input matrix of shape ``(n, p)``
+    C : array_like
+        Output matrix of shape ``(q, n)``
+    D : array_like
+        Feedthrough (or feedforward) matrix of shape ``(q, p)``
+    input : int, optional
+        For multiple-input systems, the index of the input to use.
+
+    Returns
+    -------
+    z, p : sequence
+        Zeros and poles.
+    k : float
+        System gain.
+
+    """
+    return tf2zpk(*ss2tf(A, B, C, D, input=input))
+
+
+def cont2discrete(system, dt, method="zoh", alpha=None):
+    """
+    Transform a continuous to a discrete state-space system.
+
+    Parameters
+    ----------
+    system : a tuple describing the system or an instance of `lti`
+        The following gives the number of elements in the tuple and
+        the interpretation:
+
+            * 1: (instance of `lti`)
+            * 2: (num, den)
+            * 3: (zeros, poles, gain)
+            * 4: (A, B, C, D)
+
+    dt : float
+        The discretization time step.
+    method : str, optional
+        Which method to use:
+
+            * gbt: generalized bilinear transformation
+            * bilinear: Tustin's approximation ("gbt" with alpha=0.5)
+            * euler: Euler (or forward differencing) method ("gbt" with alpha=0)
+            * backward_diff: Backwards differencing ("gbt" with alpha=1.0)
+            * zoh: zero-order hold (default)
+            * foh: first-order hold (*versionadded: 1.3.0*)
+            * impulse: equivalent impulse response (*versionadded: 1.3.0*)
+
+    alpha : float within [0, 1], optional
+        The generalized bilinear transformation weighting parameter, which
+        should only be specified with method="gbt", and is ignored otherwise
+
+    Returns
+    -------
+    sysd : tuple containing the discrete system
+        Based on the input type, the output will be of the form
+
+        * (num, den, dt)   for transfer function input
+        * (zeros, poles, gain, dt)   for zeros-poles-gain input
+        * (A, B, C, D, dt) for state-space system input
+
+    Notes
+    -----
+    By default, the routine uses a Zero-Order Hold (zoh) method to perform
+    the transformation. Alternatively, a generalized bilinear transformation
+    may be used, which includes the common Tustin's bilinear approximation,
+    an Euler's method technique, or a backwards differencing technique.
+
+    The Zero-Order Hold (zoh) method is based on [1]_, the generalized bilinear
+    approximation is based on [2]_ and [3]_, the First-Order Hold (foh) method
+    is based on [4]_.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models
+
+    .. [2] http://techteach.no/publications/discretetime_signals_systems/discrete.pdf
+
+    .. [3] G. Zhang, X. Chen, and T. Chen, Digital redesign via the generalized
+        bilinear transformation, Int. J. Control, vol. 82, no. 4, pp. 741-754,
+        2009.
+        (https://www.mypolyuweb.hk/~magzhang/Research/ZCC09_IJC.pdf)
+
+    .. [4] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital control
+        of dynamic systems, 3rd ed. Menlo Park, Calif: Addison-Wesley,
+        pp. 204-206, 1998.
+
+    """
+    if len(system) == 1:
+        return system.to_discrete()
+    if len(system) == 2:
+        sysd = cont2discrete(tf2ss(system[0], system[1]), dt, method=method,
+                             alpha=alpha)
+        return ss2tf(sysd[0], sysd[1], sysd[2], sysd[3]) + (dt,)
+    elif len(system) == 3:
+        sysd = cont2discrete(zpk2ss(system[0], system[1], system[2]), dt,
+                             method=method, alpha=alpha)
+        return ss2zpk(sysd[0], sysd[1], sysd[2], sysd[3]) + (dt,)
+    elif len(system) == 4:
+        a, b, c, d = system
+    else:
+        raise ValueError("First argument must either be a tuple of 2 (tf), "
+                         "3 (zpk), or 4 (ss) arrays.")
+
+    if method == 'gbt':
+        if alpha is None:
+            raise ValueError("Alpha parameter must be specified for the "
+                             "generalized bilinear transform (gbt) method")
+        elif alpha < 0 or alpha > 1:
+            raise ValueError("Alpha parameter must be within the interval "
+                             "[0,1] for the gbt method")
+
+    if method == 'gbt':
+        # This parameter is used repeatedly - compute once here
+        ima = np.eye(a.shape[0]) - alpha*dt*a
+        ad = linalg.solve(ima, np.eye(a.shape[0]) + (1.0-alpha)*dt*a)
+        bd = linalg.solve(ima, dt*b)
+
+        # Similarly solve for the output equation matrices
+        cd = linalg.solve(ima.transpose(), c.transpose())
+        cd = cd.transpose()
+        dd = d + alpha*np.dot(c, bd)
+
+    elif method == 'bilinear' or method == 'tustin':
+        return cont2discrete(system, dt, method="gbt", alpha=0.5)
+
+    elif method == 'euler' or method == 'forward_diff':
+        return cont2discrete(system, dt, method="gbt", alpha=0.0)
+
+    elif method == 'backward_diff':
+        return cont2discrete(system, dt, method="gbt", alpha=1.0)
+
+    elif method == 'zoh':
+        # Build an exponential matrix
+        em_upper = np.hstack((a, b))
+
+        # Need to stack zeros under the a and b matrices
+        em_lower = np.hstack((np.zeros((b.shape[1], a.shape[0])),
+                              np.zeros((b.shape[1], b.shape[1]))))
+
+        em = np.vstack((em_upper, em_lower))
+        ms = linalg.expm(dt * em)
+
+        # Dispose of the lower rows
+        ms = ms[:a.shape[0], :]
+
+        ad = ms[:, 0:a.shape[1]]
+        bd = ms[:, a.shape[1]:]
+
+        cd = c
+        dd = d
+
+    elif method == 'foh':
+        # Size parameters for convenience
+        n = a.shape[0]
+        m = b.shape[1]
+
+        # Build an exponential matrix similar to 'zoh' method
+        em_upper = linalg.block_diag(np.block([a, b]) * dt, np.eye(m))
+        em_lower = zeros((m, n + 2 * m))
+        em = np.block([[em_upper], [em_lower]])
+
+        ms = linalg.expm(em)
+
+        # Get the three blocks from upper rows
+        ms11 = ms[:n, 0:n]
+        ms12 = ms[:n, n:n + m]
+        ms13 = ms[:n, n + m:]
+
+        ad = ms11
+        bd = ms12 - ms13 + ms11 @ ms13
+        cd = c
+        dd = d + c @ ms13
+
+    elif method == 'impulse':
+        if not np.allclose(d, 0):
+            raise ValueError("Impulse method is only applicable"
+                             "to strictly proper systems")
+
+        ad = linalg.expm(a * dt)
+        bd = ad @ b * dt
+        cd = c
+        dd = c @ b * dt
+
+    else:
+        raise ValueError("Unknown transformation method '%s'" % method)
+
+    return ad, bd, cd, dd, dt

venv/Lib/site-packages/scipy/signal/setup.py

@@ -0,0 +1,42 @@
+from scipy._build_utils import numpy_nodepr_api
+
+
+def configuration(parent_package='', top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    from scipy._build_utils.compiler_helper import set_c_flags_hook
+
+    config = Configuration('signal', parent_package, top_path)
+
+    config.add_data_dir('tests')
+
+    config.add_subpackage('windows')
+
+    sigtools = config.add_extension('sigtools',
+                         sources=['sigtoolsmodule.c', 'firfilter.c',
+                                  'medianfilter.c', 'lfilter.c.src',
+                                  'correlate_nd.c.src'],
+                         depends=['sigtools.h'],
+                         include_dirs=['.'],
+                         **numpy_nodepr_api)
+    sigtools._pre_build_hook = set_c_flags_hook
+
+    config.add_extension(
+        '_spectral', sources=['_spectral.c'])
+    config.add_extension(
+        '_max_len_seq_inner', sources=['_max_len_seq_inner.c'])
+    config.add_extension(
+        '_peak_finding_utils', sources=['_peak_finding_utils.c'])
+    config.add_extension(
+        '_sosfilt', sources=['_sosfilt.c'])
+    config.add_extension(
+        '_upfirdn_apply', sources=['_upfirdn_apply.c'])
+    spline_src = ['splinemodule.c', 'S_bspline_util.c', 'D_bspline_util.c',
+                  'C_bspline_util.c', 'Z_bspline_util.c', 'bspline_util.c']
+    config.add_extension('spline', sources=spline_src, **numpy_nodepr_api)
+
+    return config
+
+
+if __name__ == '__main__':
+    from numpy.distutils.core import setup
+    setup(**configuration(top_path='').todict())

venv/Lib/site-packages/scipy/signal/tests/mpsig.py

@@ -0,0 +1,122 @@
+"""
+Some signal functions implemented using mpmath.
+"""
+
+try:
+    import mpmath  # type: ignore[import]
+except ImportError:
+    mpmath = None
+
+
+def _prod(seq):
+    """Returns the product of the elements in the sequence `seq`."""
+    p = 1
+    for elem in seq:
+        p *= elem
+    return p
+
+
+def _relative_degree(z, p):
+    """
+    Return relative degree of transfer function from zeros and poles.
+
+    This is simply len(p) - len(z), which must be nonnegative.
+    A ValueError is raised if len(p) < len(z).
+    """
+    degree = len(p) - len(z)
+    if degree < 0:
+        raise ValueError("Improper transfer function. "
+                         "Must have at least as many poles as zeros.")
+    return degree
+
+
+def _zpkbilinear(z, p, k, fs):
+    """Bilinear transformation to convert a filter from analog to digital."""
+
+    degree = _relative_degree(z, p)
+
+    fs2 = 2*fs
+
+    # Bilinear transform the poles and zeros
+    z_z = [(fs2 + z1) / (fs2 - z1) for z1 in z]
+    p_z = [(fs2 + p1) / (fs2 - p1) for p1 in p]
+
+    # Any zeros that were at infinity get moved to the Nyquist frequency
+    z_z.extend([-1] * degree)
+
+    # Compensate for gain change
+    numer = _prod(fs2 - z1 for z1 in z)
+    denom = _prod(fs2 - p1 for p1 in p)
+    k_z = k * numer / denom
+
+    return z_z, p_z, k_z.real
+
+
+def _zpklp2lp(z, p, k, wo=1):
+    """Transform a lowpass filter to a different cutoff frequency."""
+
+    degree = _relative_degree(z, p)
+
+    # Scale all points radially from origin to shift cutoff frequency
+    z_lp = [wo * z1 for z1 in z]
+    p_lp = [wo * p1 for p1 in p]
+
+    # Each shifted pole decreases gain by wo, each shifted zero increases it.
+    # Cancel out the net change to keep overall gain the same
+    k_lp = k * wo**degree
+
+    return z_lp, p_lp, k_lp
+
+
+def _butter_analog_poles(n):
+    """
+    Poles of an analog Butterworth lowpass filter.
+
+    This is the same calculation as scipy.signal.buttap(n) or
+    scipy.signal.butter(n, 1, analog=True, output='zpk'), but mpmath is used,
+    and only the poles are returned.
+    """
+    poles = [-mpmath.exp(1j*mpmath.pi*k/(2*n)) for k in range(-n+1, n, 2)]
+    return poles
+
+
+def butter_lp(n, Wn):
+    """
+    Lowpass Butterworth digital filter design.
+
+    This computes the same result as scipy.signal.butter(n, Wn, output='zpk'),
+    but it uses mpmath, and the results are returned in lists instead of NumPy
+    arrays.
+    """
+    zeros = []
+    poles = _butter_analog_poles(n)
+    k = 1
+    fs = 2
+    warped = 2 * fs * mpmath.tan(mpmath.pi * Wn / fs)
+    z, p, k = _zpklp2lp(zeros, poles, k, wo=warped)
+    z, p, k = _zpkbilinear(z, p, k, fs=fs)
+    return z, p, k
+
+
+def zpkfreqz(z, p, k, worN=None):
+    """
+    Frequency response of a filter in zpk format, using mpmath.
+
+    This is the same calculation as scipy.signal.freqz, but the input is in
+    zpk format, the calculation is performed using mpath, and the results are
+    returned in lists instead of NumPy arrays.
+    """
+    if worN is None or isinstance(worN, int):
+        N = worN or 512
+        ws = [mpmath.pi * mpmath.mpf(j) / N for j in range(N)]
+    else:
+        ws = worN
+
+    h = []
+    for wk in ws:
+        zm1 = mpmath.exp(1j * wk)
+        numer = _prod([zm1 - t for t in z])
+        denom = _prod([zm1 - t for t in p])
+        hk = k * numer / denom
+        h.append(hk)
+    return ws, h

venv/Lib/site-packages/scipy/signal/tests/test_array_tools.py

@@ -0,0 +1,111 @@
+import numpy as np
+
+from numpy.testing import assert_array_equal
+from pytest import raises as assert_raises
+
+from scipy.signal._arraytools import (axis_slice, axis_reverse,
+     odd_ext, even_ext, const_ext, zero_ext)
+
+
+class TestArrayTools(object):
+
+    def test_axis_slice(self):
+        a = np.arange(12).reshape(3, 4)
+
+        s = axis_slice(a, start=0, stop=1, axis=0)
+        assert_array_equal(s, a[0:1, :])
+
+        s = axis_slice(a, start=-1, axis=0)
+        assert_array_equal(s, a[-1:, :])
+
+        s = axis_slice(a, start=0, stop=1, axis=1)
+        assert_array_equal(s, a[:, 0:1])
+
+        s = axis_slice(a, start=-1, axis=1)
+        assert_array_equal(s, a[:, -1:])
+
+        s = axis_slice(a, start=0, step=2, axis=0)
+        assert_array_equal(s, a[::2, :])
+
+        s = axis_slice(a, start=0, step=2, axis=1)
+        assert_array_equal(s, a[:, ::2])
+
+    def test_axis_reverse(self):
+        a = np.arange(12).reshape(3, 4)
+
+        r = axis_reverse(a, axis=0)
+        assert_array_equal(r, a[::-1, :])
+
+        r = axis_reverse(a, axis=1)
+        assert_array_equal(r, a[:, ::-1])
+
+    def test_odd_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        odd = odd_ext(a, 2, axis=1)
+        expected = np.array([[-1, 0, 1, 2, 3, 4, 5, 6, 7],
+                             [11, 10, 9, 8, 7, 6, 5, 4, 3]])
+        assert_array_equal(odd, expected)
+
+        odd = odd_ext(a, 1, axis=0)
+        expected = np.array([[-7, -4, -1, 2, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [17, 14, 11, 8, 5]])
+        assert_array_equal(odd, expected)
+
+        assert_raises(ValueError, odd_ext, a, 2, axis=0)
+        assert_raises(ValueError, odd_ext, a, 5, axis=1)
+
+    def test_even_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        even = even_ext(a, 2, axis=1)
+        expected = np.array([[3, 2, 1, 2, 3, 4, 5, 4, 3],
+                             [7, 8, 9, 8, 7, 6, 5, 6, 7]])
+        assert_array_equal(even, expected)
+
+        even = even_ext(a, 1, axis=0)
+        expected = np.array([[9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [1, 2, 3, 4, 5]])
+        assert_array_equal(even, expected)
+
+        assert_raises(ValueError, even_ext, a, 2, axis=0)
+        assert_raises(ValueError, even_ext, a, 5, axis=1)
+
+    def test_const_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        const = const_ext(a, 2, axis=1)
+        expected = np.array([[1, 1, 1, 2, 3, 4, 5, 5, 5],
+                             [9, 9, 9, 8, 7, 6, 5, 5, 5]])
+        assert_array_equal(const, expected)
+
+        const = const_ext(a, 1, axis=0)
+        expected = np.array([[1, 2, 3, 4, 5],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [9, 8, 7, 6, 5]])
+        assert_array_equal(const, expected)
+
+    def test_zero_ext(self):
+        a = np.array([[1, 2, 3, 4, 5],
+                      [9, 8, 7, 6, 5]])
+
+        zero = zero_ext(a, 2, axis=1)
+        expected = np.array([[0, 0, 1, 2, 3, 4, 5, 0, 0],
+                             [0, 0, 9, 8, 7, 6, 5, 0, 0]])
+        assert_array_equal(zero, expected)
+
+        zero = zero_ext(a, 1, axis=0)
+        expected = np.array([[0, 0, 0, 0, 0],
+                             [1, 2, 3, 4, 5],
+                             [9, 8, 7, 6, 5],
+                             [0, 0, 0, 0, 0]])
+        assert_array_equal(zero, expected)
+

venv/Lib/site-packages/scipy/signal/tests/test_bsplines.py

@@ -0,0 +1,222 @@
+# pylint: disable=missing-docstring
+import numpy as np
+from numpy import array
+from numpy.testing import (assert_equal,
+                           assert_allclose, assert_array_equal,
+                           assert_almost_equal)
+from pytest import raises
+
+import scipy.signal.bsplines as bsp
+
+
+class TestBSplines(object):
+    """Test behaviors of B-splines. The values tested against were returned as of
+    SciPy 1.1.0 and are included for regression testing purposes"""
+
+    def test_factorial(self):
+        # can't all be zero state
+        assert_equal(bsp.factorial(1), 1)
+
+    def test_spline_filter(self):
+        np.random.seed(12457)
+        # Test the type-error branch
+        raises(TypeError, bsp.spline_filter, array([0]), 0)
+        # Test the complex branch
+        data_array_complex = np.random.rand(7, 7) + np.random.rand(7, 7)*1j
+        # make the magnitude exceed 1, and make some negative
+        data_array_complex = 10*(1+1j-2*data_array_complex)
+        result_array_complex = array(
+            [[-4.61489230e-01-1.92994022j, 8.33332443+6.25519943j,
+              6.96300745e-01-9.05576038j, 5.28294849+3.97541356j,
+              5.92165565+7.68240595j, 6.59493160-1.04542804j,
+              9.84503460-5.85946894j],
+             [-8.78262329-8.4295969j, 7.20675516+5.47528982j,
+              -8.17223072+2.06330729j, -4.38633347-8.65968037j,
+              9.89916801-8.91720295j, 2.67755103+8.8706522j,
+              6.24192142+3.76879835j],
+             [-3.15627527+2.56303072j, 9.87658501-0.82838702j,
+              -9.96930313+8.72288895j, 3.17193985+6.42474651j,
+              -4.50919819-6.84576082j, 5.75423431+9.94723988j,
+              9.65979767+6.90665293j],
+             [-8.28993416-6.61064005j, 9.71416473e-01-9.44907284j,
+              -2.38331890+9.25196648j, -7.08868170-0.77403212j,
+              4.89887714+7.05371094j, -1.37062311-2.73505688j,
+              7.70705748+2.5395329j],
+             [2.51528406-1.82964492j, 3.65885472+2.95454836j,
+              5.16786575-1.66362023j, -8.77737999e-03+5.72478867j,
+              4.10533333-3.10287571j, 9.04761887+1.54017115j,
+              -5.77960968e-01-7.87758923j],
+             [9.86398506-3.98528528j, -4.71444130-2.44316983j,
+              -1.68038976-1.12708664j, 2.84695053+1.01725709j,
+              1.14315915-8.89294529j, -3.17127085-5.42145538j,
+              1.91830420-6.16370344j],
+             [7.13875294+2.91851187j, -5.35737514+9.64132309j,
+              -9.66586399+0.70250005j, -9.87717438-2.0262239j,
+              9.93160629+1.5630846j, 4.71948051-2.22050714j,
+              9.49550819+7.8995142j]])
+        # FIXME: for complex types, the computations are done in
+        # single precision (reason unclear). When this is changed,
+        # this test needs updating.
+        assert_allclose(bsp.spline_filter(data_array_complex, 0),
+                        result_array_complex, rtol=1e-6)
+        # Test the real branch
+        np.random.seed(12457)
+        data_array_real = np.random.rand(12, 12)
+        # make the magnitude exceed 1, and make some negative
+        data_array_real = 10*(1-2*data_array_real)
+        result_array_real = array(
+            [[-.463312621, 8.33391222, .697290949, 5.28390836,
+              5.92066474, 6.59452137, 9.84406950, -8.78324188,
+              7.20675750, -8.17222994, -4.38633345, 9.89917069],
+             [2.67755154, 6.24192170, -3.15730578, 9.87658581,
+              -9.96930425, 3.17194115, -4.50919947, 5.75423446,
+              9.65979824, -8.29066885, .971416087, -2.38331897],
+             [-7.08868346, 4.89887705, -1.37062289, 7.70705838,
+              2.51526461, 3.65885497, 5.16786604, -8.77715342e-03,
+              4.10533325, 9.04761993, -.577960351, 9.86382519],
+             [-4.71444301, -1.68038985, 2.84695116, 1.14315938,
+              -3.17127091, 1.91830461, 7.13779687, -5.35737482,
+              -9.66586425, -9.87717456, 9.93160672, 4.71948144],
+             [9.49551194, -1.92958436, 6.25427993, -9.05582911,
+              3.97562282, 7.68232426, -1.04514824, -5.86021443,
+              -8.43007451, 5.47528997, 2.06330736, -8.65968112],
+             [-8.91720100, 8.87065356, 3.76879937, 2.56222894,
+              -.828387146, 8.72288903, 6.42474741, -6.84576083,
+              9.94724115, 6.90665380, -6.61084494, -9.44907391],
+             [9.25196790, -.774032030, 7.05371046, -2.73505725,
+              2.53953305, -1.82889155, 2.95454824, -1.66362046,
+              5.72478916, -3.10287679, 1.54017123, -7.87759020],
+             [-3.98464539, -2.44316992, -1.12708657, 1.01725672,
+              -8.89294671, -5.42145629, -6.16370321, 2.91775492,
+              9.64132208, .702499998, -2.02622392, 1.56308431],
+             [-2.22050773, 7.89951554, 5.98970713, -7.35861835,
+              5.45459283, -7.76427957, 3.67280490, -4.05521315,
+              4.51967507, -3.22738749, -3.65080177, 3.05630155],
+             [-6.21240584, -.296796126, -8.34800163, 9.21564563,
+              -3.61958784, -4.77120006, -3.99454057, 1.05021988e-03,
+              -6.95982829, 6.04380797, 8.43181250, -2.71653339],
+             [1.19638037, 6.99718842e-02, 6.72020394, -2.13963198,
+              3.75309875, -5.70076744, 5.92143551, -7.22150575,
+              -3.77114594, -1.11903194, -5.39151466, 3.06620093],
+             [9.86326886, 1.05134482, -7.75950607, -3.64429655,
+              7.81848957, -9.02270373, 3.73399754, -4.71962549,
+              -7.71144306, 3.78263161, 6.46034818, -4.43444731]])
+        assert_allclose(bsp.spline_filter(data_array_real, 0),
+                        result_array_real)
+
+    def test_bspline(self):
+        np.random.seed(12458)
+        assert_allclose(bsp.bspline(np.random.rand(1, 1), 2),
+                        array([[0.73694695]]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        data_array_complex = 0.1*data_array_complex
+        result_array_complex = array(
+            [[0.40882362, 0.41021151, 0.40886708, 0.40905103],
+             [0.40829477, 0.41021230, 0.40966097, 0.40939871],
+             [0.41036803, 0.40901724, 0.40965331, 0.40879513],
+             [0.41032862, 0.40925287, 0.41037754, 0.41027477]])
+        assert_allclose(bsp.bspline(data_array_complex, 10),
+                        result_array_complex)
+
+    def test_gauss_spline(self):
+        np.random.seed(12459)
+        assert_almost_equal(bsp.gauss_spline(0, 0), 1.381976597885342)
+        assert_allclose(bsp.gauss_spline(array([1.]), 1), array([0.04865217]))
+
+    def test_cubic(self):
+        np.random.seed(12460)
+        assert_array_equal(bsp.cubic([0]), array([0]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        data_array_complex = 1+1j-2*data_array_complex
+        # scaling the magnitude by 10 makes the results close enough to zero,
+        # that the assertion fails, so just make the elements have a mix of
+        # positive and negative imaginary components...
+        result_array_complex = array(
+            [[0.23056563, 0.38414406, 0.08342987, 0.06904847],
+             [0.17240848, 0.47055447, 0.63896278, 0.39756424],
+             [0.12672571, 0.65862632, 0.1116695, 0.09700386],
+             [0.3544116, 0.17856518, 0.1528841, 0.17285762]])
+        assert_allclose(bsp.cubic(data_array_complex), result_array_complex)
+
+    def test_quadratic(self):
+        np.random.seed(12461)
+        assert_array_equal(bsp.quadratic([0]), array([0]))
+        data_array_complex = np.random.rand(4, 4) + np.random.rand(4, 4)*1j
+        # scaling the magnitude by 10 makes the results all zero,
+        # so just make the elements have a mix of positive and negative
+        # imaginary components...
+        data_array_complex = (1+1j-2*data_array_complex)
+        result_array_complex = array(
+            [[0.23062746, 0.06338176, 0.34902312, 0.31944105],
+             [0.14701256, 0.13277773, 0.29428615, 0.09814697],
+             [0.52873842, 0.06484157, 0.09517566, 0.46420389],
+             [0.09286829, 0.09371954, 0.1422526, 0.16007024]])
+        assert_allclose(bsp.quadratic(data_array_complex),
+                        result_array_complex)
+
+    def test_cspline1d(self):
+        np.random.seed(12462)
+        assert_array_equal(bsp.cspline1d(array([0])), [0.])
+        c1d = array([1.21037185, 1.86293902, 2.98834059, 4.11660378,
+                     4.78893826])
+        # test lamda != 0
+        assert_allclose(bsp.cspline1d(array([1., 2, 3, 4, 5]), 1), c1d)
+        c1d0 = array([0.78683946, 2.05333735, 2.99981113, 3.94741812,
+                      5.21051638])
+        assert_allclose(bsp.cspline1d(array([1., 2, 3, 4, 5])), c1d0)
+
+    def test_qspline1d(self):
+        np.random.seed(12463)
+        assert_array_equal(bsp.qspline1d(array([0])), [0.])
+        # test lamda != 0
+        raises(ValueError, bsp.qspline1d, array([1., 2, 3, 4, 5]), 1.)
+        raises(ValueError, bsp.qspline1d, array([1., 2, 3, 4, 5]), -1.)
+        q1d0 = array([0.85350007, 2.02441743, 2.99999534, 3.97561055,
+                      5.14634135])
+        assert_allclose(bsp.qspline1d(array([1., 2, 3, 4, 5])), q1d0)
+
+    def test_cspline1d_eval(self):
+        np.random.seed(12464)
+        assert_allclose(bsp.cspline1d_eval(array([0., 0]), [0.]), array([0.]))
+        assert_array_equal(bsp.cspline1d_eval(array([1., 0, 1]), []),
+                           array([]))
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1]-x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = array([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                   1.396, 4.094])
+        cj = bsp.cspline1d(y)
+        newy = array([6.203, 4.41570658, 3.514, 5.16924703, 6.864, 6.04643068,
+                      4.21600281, 6.04643068, 6.864, 5.16924703, 3.514,
+                      4.41570658, 6.203, 6.80717667, 6.759, 6.98971173, 7.433,
+                      7.79560142, 7.874, 7.41525761, 5.879, 3.18686814, 1.396,
+                      2.24889482, 4.094, 2.24889482, 1.396, 3.18686814, 5.879,
+                      7.41525761, 7.874, 7.79560142, 7.433, 6.98971173, 6.759,
+                      6.80717667, 6.203, 4.41570658])
+        assert_allclose(bsp.cspline1d_eval(cj, newx, dx=dx, x0=x[0]), newy)
+
+    def test_qspline1d_eval(self):
+        np.random.seed(12465)
+        assert_allclose(bsp.qspline1d_eval(array([0., 0]), [0.]), array([0.]))
+        assert_array_equal(bsp.qspline1d_eval(array([1., 0, 1]), []),
+                           array([]))
+        x = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
+        dx = x[1]-x[0]
+        newx = [-6., -5.5, -5., -4.5, -4., -3.5, -3., -2.5, -2., -1.5, -1.,
+                -0.5, 0., 0.5, 1., 1.5, 2., 2.5, 3., 3.5, 4., 4.5, 5., 5.5, 6.,
+                6.5, 7., 7.5, 8., 8.5, 9., 9.5, 10., 10.5, 11., 11.5, 12.,
+                12.5]
+        y = array([4.216, 6.864, 3.514, 6.203, 6.759, 7.433, 7.874, 5.879,
+                   1.396, 4.094])
+        cj = bsp.qspline1d(y)
+        newy = array([6.203, 4.49418159, 3.514, 5.18390821, 6.864, 5.91436915,
+                      4.21600002, 5.91436915, 6.864, 5.18390821, 3.514,
+                      4.49418159, 6.203, 6.71900226, 6.759, 7.03980488, 7.433,
+                      7.81016848, 7.874, 7.32718426, 5.879, 3.23872593, 1.396,
+                      2.34046013, 4.094, 2.34046013, 1.396, 3.23872593, 5.879,
+                      7.32718426, 7.874, 7.81016848, 7.433, 7.03980488, 6.759,
+                      6.71900226, 6.203, 4.49418159])
+        assert_allclose(bsp.qspline1d_eval(cj, newx, dx=dx, x0=x[0]), newy)

venv/Lib/site-packages/scipy/signal/tests/test_cont2discrete.py

@@ -0,0 +1,420 @@
+import numpy as np
+from numpy.testing import \
+                          assert_array_almost_equal, assert_almost_equal, \
+                          assert_allclose, assert_equal
+
+import pytest
+from scipy.signal import cont2discrete as c2d
+from scipy.signal import dlsim, ss2tf, ss2zpk, lsim2, lti
+from scipy.signal import tf2ss, impulse2, dimpulse, step2, dstep
+
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# March 29, 2011
+
+
+class TestC2D(object):
+    def test_zoh(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.324360635350064)
+        # c and d in discrete should be equal to their continuous counterparts
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cc, cd)
+        assert_array_almost_equal(dc, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_foh(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.420839287058789)
+        cd_truth = cc
+        dd_truth = np.array([[0.260262223725224],
+                             [0.297442541400256],
+                             [-0.144098411624840]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='foh')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_impulse(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [0.0]])
+
+        # True values are verified with Matlab
+        ad_truth = 1.648721270700128 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.412180317675032)
+        cd_truth = cc
+        dd_truth = np.array([[0.4375], [0.5], [0.3125]])
+        dt_requested = 0.5
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='impulse')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_gbt(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+        alpha = 1.0 / 3.0
+
+        ad_truth = 1.6 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.3)
+        cd_truth = np.array([[0.9, 1.2],
+                             [1.2, 1.2],
+                             [1.2, 0.3]])
+        dd_truth = np.array([[0.175],
+                             [0.2],
+                             [-0.205]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='gbt', alpha=alpha)
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_euler(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 1.5 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.25)
+        cd_truth = np.array([[0.75, 1.0],
+                             [1.0, 1.0],
+                             [1.0, 0.25]])
+        dd_truth = dc
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='euler')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_backward_diff(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = 2.0 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.5)
+        cd_truth = np.array([[1.5, 2.0],
+                             [2.0, 2.0],
+                             [2.0, 0.5]])
+        dd_truth = np.array([[0.875],
+                             [1.0],
+                             [0.295]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='backward_diff')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+
+    def test_bilinear(self):
+        ac = np.eye(2)
+        bc = np.full((2, 1), 0.5)
+        cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
+        dc = np.array([[0.0], [0.0], [-0.33]])
+
+        dt_requested = 0.5
+
+        ad_truth = (5.0 / 3.0) * np.eye(2)
+        bd_truth = np.full((2, 1), 1.0 / 3.0)
+        cd_truth = np.array([[1.0, 4.0 / 3.0],
+                             [4.0 / 3.0, 4.0 / 3.0],
+                             [4.0 / 3.0, 1.0 / 3.0]])
+        dd_truth = np.array([[0.291666666666667],
+                             [1.0 / 3.0],
+                             [-0.121666666666667]])
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+        # Same continuous system again, but change sampling rate
+
+        ad_truth = 1.4 * np.eye(2)
+        bd_truth = np.full((2, 1), 0.2)
+        cd_truth = np.array([[0.9, 1.2], [1.2, 1.2], [1.2, 0.3]])
+        dd_truth = np.array([[0.175], [0.2], [-0.205]])
+
+        dt_requested = 1.0 / 3.0
+
+        ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
+                                 method='bilinear')
+
+        assert_array_almost_equal(ad_truth, ad)
+        assert_array_almost_equal(bd_truth, bd)
+        assert_array_almost_equal(cd_truth, cd)
+        assert_array_almost_equal(dd_truth, dd)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_transferfunction(self):
+        numc = np.array([0.25, 0.25, 0.5])
+        denc = np.array([0.75, 0.75, 1.0])
+
+        numd = np.array([[1.0 / 3.0, -0.427419169438754, 0.221654141101125]])
+        dend = np.array([1.0, -1.351394049721225, 0.606530659712634])
+
+        dt_requested = 0.5
+
+        num, den, dt = c2d((numc, denc), dt_requested, method='zoh')
+
+        assert_array_almost_equal(numd, num)
+        assert_array_almost_equal(dend, den)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_zerospolesgain(self):
+        zeros_c = np.array([0.5, -0.5])
+        poles_c = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
+        k_c = 1.0
+
+        zeros_d = [1.23371727305860, 0.735356894461267]
+        polls_d = [0.938148335039729 + 0.346233593780536j,
+                   0.938148335039729 - 0.346233593780536j]
+        k_d = 1.0
+
+        dt_requested = 0.5
+
+        zeros, poles, k, dt = c2d((zeros_c, poles_c, k_c), dt_requested,
+                                  method='zoh')
+
+        assert_array_almost_equal(zeros_d, zeros)
+        assert_array_almost_equal(polls_d, poles)
+        assert_almost_equal(k_d, k)
+        assert_almost_equal(dt_requested, dt)
+
+    def test_gbt_with_sio_tf_and_zpk(self):
+        """Test method='gbt' with alpha=0.25 for tf and zpk cases."""
+        # State space coefficients for the continuous SIO system.
+        A = -1.0
+        B = 1.0
+        C = 1.0
+        D = 0.5
+
+        # The continuous transfer function coefficients.
+        cnum, cden = ss2tf(A, B, C, D)
+
+        # Continuous zpk representation
+        cz, cp, ck = ss2zpk(A, B, C, D)
+
+        h = 1.0
+        alpha = 0.25
+
+        # Explicit formulas, in the scalar case.
+        Ad = (1 + (1 - alpha) * h * A) / (1 - alpha * h * A)
+        Bd = h * B / (1 - alpha * h * A)
+        Cd = C / (1 - alpha * h * A)
+        Dd = D + alpha * C * Bd
+
+        # Convert the explicit solution to tf
+        dnum, dden = ss2tf(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete tf using cont2discrete.
+        c2dnum, c2dden, dt = c2d((cnum, cden), h, method='gbt', alpha=alpha)
+
+        assert_allclose(dnum, c2dnum)
+        assert_allclose(dden, c2dden)
+
+        # Convert explicit solution to zpk.
+        dz, dp, dk = ss2zpk(Ad, Bd, Cd, Dd)
+
+        # Compute the discrete zpk using cont2discrete.
+        c2dz, c2dp, c2dk, dt = c2d((cz, cp, ck), h, method='gbt', alpha=alpha)
+
+        assert_allclose(dz, c2dz)
+        assert_allclose(dp, c2dp)
+        assert_allclose(dk, c2dk)
+
+    def test_discrete_approx(self):
+        """
+        Test that the solution to the discrete approximation of a continuous
+        system actually approximates the solution to the continuous system.
+        This is an indirect test of the correctness of the implementation
+        of cont2discrete.
+        """
+
+        def u(t):
+            return np.sin(2.5 * t)
+
+        a = np.array([[-0.01]])
+        b = np.array([[1.0]])
+        c = np.array([[1.0]])
+        d = np.array([[0.2]])
+        x0 = 1.0
+
+        t = np.linspace(0, 10.0, 101)
+        dt = t[1] - t[0]
+        u1 = u(t)
+
+        # Use lsim2 to compute the solution to the continuous system.
+        t, yout, xout = lsim2((a, b, c, d), T=t, U=u1, X0=x0,
+                              rtol=1e-9, atol=1e-11)
+
+        # Convert the continuous system to a discrete approximation.
+        dsys = c2d((a, b, c, d), dt, method='bilinear')
+
+        # Use dlsim with the pairwise averaged input to compute the output
+        # of the discrete system.
+        u2 = 0.5 * (u1[:-1] + u1[1:])
+        t2 = t[:-1]
+        td2, yd2, xd2 = dlsim(dsys, u=u2.reshape(-1, 1), t=t2, x0=x0)
+
+        # ymid is the average of consecutive terms of the "exact" output
+        # computed by lsim2.  This is what the discrete approximation
+        # actually approximates.
+        ymid = 0.5 * (yout[:-1] + yout[1:])
+
+        assert_allclose(yd2.ravel(), ymid, rtol=1e-4)
+
+    def test_simo_tf(self):
+        # See gh-5753
+        tf = ([[1, 0], [1, 1]], [1, 1])
+        num, den, dt = c2d(tf, 0.01)
+
+        assert_equal(dt, 0.01)  # sanity check
+        assert_allclose(den, [1, -0.990404983], rtol=1e-3)
+        assert_allclose(num, [[1, -1], [1, -0.99004983]], rtol=1e-3)
+
+    def test_multioutput(self):
+        ts = 0.01  # time step
+
+        tf = ([[1, -3], [1, 5]], [1, 1])
+        num, den, dt = c2d(tf, ts)
+
+        tf1 = (tf[0][0], tf[1])
+        num1, den1, dt1 = c2d(tf1, ts)
+
+        tf2 = (tf[0][1], tf[1])
+        num2, den2, dt2 = c2d(tf2, ts)
+
+        # Sanity checks
+        assert_equal(dt, dt1)
+        assert_equal(dt, dt2)
+
+        # Check that we get the same results
+        assert_allclose(num, np.vstack((num1, num2)), rtol=1e-13)
+
+        # Single input, so the denominator should
+        # not be multidimensional like the numerator
+        assert_allclose(den, den1, rtol=1e-13)
+        assert_allclose(den, den2, rtol=1e-13)
+
+class TestC2dLti(object):
+    def test_c2d_ss(self):
+        # StateSpace
+        A = np.array([[-0.3, 0.1], [0.2, -0.7]])
+        B = np.array([[0], [1]])
+        C = np.array([[1, 0]])
+        D = 0
+
+        A_res = np.array([[0.985136404135682, 0.004876671474795],
+                          [0.009753342949590, 0.965629718236502]])
+        B_res = np.array([[0.000122937599964], [0.049135527547844]])
+
+        sys_ssc = lti(A, B, C, D)
+        sys_ssd = sys_ssc.to_discrete(0.05)
+
+        assert_allclose(sys_ssd.A, A_res)
+        assert_allclose(sys_ssd.B, B_res)
+        assert_allclose(sys_ssd.C, C)
+        assert_allclose(sys_ssd.D, D)
+
+    def test_c2d_tf(self):
+
+        sys = lti([0.5, 0.3], [1.0, 0.4])
+        sys = sys.to_discrete(0.005)
+
+        # Matlab results
+        num_res = np.array([0.5, -0.485149004980066])
+        den_res = np.array([1.0, -0.980198673306755])
+
+        # Somehow a lot of numerical errors
+        assert_allclose(sys.den, den_res, atol=0.02)
+        assert_allclose(sys.num, num_res, atol=0.02)
+
+
+class TestC2dInvariants:
+    # Some test cases for checking the invariances.
+    # Array of triplets: (system, sample time, number of samples)
+    cases = [
+        (tf2ss([1, 1], [1, 1.5, 1]), 0.25, 10),
+        (tf2ss([1, 2], [1, 1.5, 3, 1]), 0.5, 10),
+        (tf2ss(0.1, [1, 1, 2, 1]), 0.5, 10),
+    ]
+
+    # Some options for lsim2 and derived routines
+    tolerances = {'rtol': 1e-9, 'atol': 1e-11}
+
+    # Check that systems discretized with the impulse-invariant
+    # method really hold the invariant
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_impulse_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont = impulse2(sys, T=time, **self.tolerances)
+        _, yout_disc = dimpulse(c2d(sys, sample_time, method='impulse'),
+                                n=len(time))
+        assert_allclose(sample_time * yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Step invariant should hold for ZOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_step_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont = step2(sys, T=time, **self.tolerances)
+        _, yout_disc = dstep(c2d(sys, sample_time, method='zoh'), n=len(time))
+        assert_allclose(yout_cont.ravel(), yout_disc[0].ravel())
+
+    # Linear invariant should hold for FOH discretized systems
+    @pytest.mark.parametrize("sys,sample_time,samples_number", cases)
+    def test_linear_invariant(self, sys, sample_time, samples_number):
+        time = np.arange(samples_number) * sample_time
+        _, yout_cont, _ = lsim2(sys, T=time, U=time, **self.tolerances)
+        _, yout_disc, _ = dlsim(c2d(sys, sample_time, method='foh'), u=time)
+        assert_allclose(yout_cont.ravel(), yout_disc.ravel())

venv/Lib/site-packages/scipy/signal/tests/test_dltisys.py

@@ -0,0 +1,598 @@
+# Author: Jeffrey Armstrong <jeff@approximatrix.com>
+# April 4, 2011
+
+import numpy as np
+from numpy.testing import (assert_equal,
+                           assert_array_almost_equal, assert_array_equal,
+                           assert_allclose, assert_, assert_almost_equal,
+                           suppress_warnings)
+from pytest import raises as assert_raises
+from scipy.signal import (dlsim, dstep, dimpulse, tf2zpk, lti, dlti,
+                          StateSpace, TransferFunction, ZerosPolesGain,
+                          dfreqresp, dbode, BadCoefficients)
+
+
+class TestDLTI(object):
+
+    def test_dlsim(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Create an input matrix with inputs down the columns (3 cols) and its
+        # respective time input vector
+        u = np.hstack((np.linspace(0, 4.0, num=5)[:, np.newaxis],
+                       np.full((5, 1), 0.01),
+                       np.full((5, 1), -0.002)))
+        t_in = np.linspace(0, 2.0, num=5)
+
+        # Define the known result
+        yout_truth = np.array([[-0.001,
+                                -0.00073,
+                                0.039446,
+                                0.0915387,
+                                0.13195948]]).T
+        xout_truth = np.asarray([[0, 0],
+                                 [0.0012, 0.0005],
+                                 [0.40233, 0.00071],
+                                 [1.163368, -0.079327],
+                                 [2.2402985, -0.3035679]])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u, t_in)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert_array_almost_equal(t_in, tout)
+
+        # Make sure input with single-dimension doesn't raise error
+        dlsim((1, 2, 3), 4)
+
+        # Interpolated control - inputs should have different time steps
+        # than the discrete model uses internally
+        u_sparse = u[[0, 4], :]
+        t_sparse = np.asarray([0.0, 2.0])
+
+        tout, yout, xout = dlsim((a, b, c, d, dt), u_sparse, t_sparse)
+
+        assert_array_almost_equal(yout_truth, yout)
+        assert_array_almost_equal(xout_truth, xout)
+        assert_equal(len(tout), yout.shape[0])
+
+        # Transfer functions (assume dt = 0.5)
+        num = np.asarray([1.0, -0.1])
+        den = np.asarray([0.3, 1.0, 0.2])
+        yout_truth = np.array([[0.0,
+                                0.0,
+                                3.33333333333333,
+                                -4.77777777777778,
+                                23.0370370370370]]).T
+
+        # Assume use of the first column of the control input built earlier
+        tout, yout = dlsim((num, den, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Retest the same with a 1-D input vector
+        uflat = np.asarray(u[:, 0])
+        uflat = uflat.reshape((5,))
+        tout, yout = dlsim((num, den, 0.5), uflat, t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # zeros-poles-gain representation
+        zd = np.array([0.5, -0.5])
+        pd = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
+        k = 1.0
+        yout_truth = np.array([[0.0, 1.0, 2.0, 2.25, 2.5]]).T
+
+        tout, yout = dlsim((zd, pd, k, 0.5), u[:, 0], t_in)
+
+        assert_array_almost_equal(yout, yout_truth)
+        assert_array_almost_equal(t_in, tout)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dlsim, system, u)
+
+    def test_dstep(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dstep should result in a tuple of three
+        # result vectors
+        yout_step_truth = (np.asarray([0.0, 0.04, 0.052, 0.0404, 0.00956,
+                                       -0.036324, -0.093318, -0.15782348,
+                                       -0.226628324, -0.2969374948]),
+                           np.asarray([-0.1, -0.075, -0.058, -0.04815,
+                                       -0.04453, -0.0461895, -0.0521812,
+                                       -0.061588875, -0.073549579,
+                                       -0.08727047595]),
+                           np.asarray([0.0, -0.01, -0.013, -0.0101, -0.00239,
+                                       0.009081, 0.0233295, 0.03945587,
+                                       0.056657081, 0.0742343737]))
+
+        tout, yout = dstep((a, b, c, d, dt), n=10)
+
+        assert_equal(len(yout), 3)
+
+        for i in range(0, len(yout)):
+            assert_equal(yout[i].shape[0], 10)
+            assert_array_almost_equal(yout[i].flatten(), yout_step_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfstep = np.asarray([0.0, 1.0, 0.0])
+        tout, yout = dstep(tfin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dstep(zpkin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfstep)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dstep, system)
+
+    def test_dimpulse(self):
+
+        a = np.asarray([[0.9, 0.1], [-0.2, 0.9]])
+        b = np.asarray([[0.4, 0.1, -0.1], [0.0, 0.05, 0.0]])
+        c = np.asarray([[0.1, 0.3]])
+        d = np.asarray([[0.0, -0.1, 0.0]])
+        dt = 0.5
+
+        # Because b.shape[1] == 3, dimpulse should result in a tuple of three
+        # result vectors
+        yout_imp_truth = (np.asarray([0.0, 0.04, 0.012, -0.0116, -0.03084,
+                                      -0.045884, -0.056994, -0.06450548,
+                                      -0.068804844, -0.0703091708]),
+                          np.asarray([-0.1, 0.025, 0.017, 0.00985, 0.00362,
+                                      -0.0016595, -0.0059917, -0.009407675,
+                                      -0.011960704, -0.01372089695]),
+                          np.asarray([0.0, -0.01, -0.003, 0.0029, 0.00771,
+                                      0.011471, 0.0142485, 0.01612637,
+                                      0.017201211, 0.0175772927]))
+
+        tout, yout = dimpulse((a, b, c, d, dt), n=10)
+
+        assert_equal(len(yout), 3)
+
+        for i in range(0, len(yout)):
+            assert_equal(yout[i].shape[0], 10)
+            assert_array_almost_equal(yout[i].flatten(), yout_imp_truth[i])
+
+        # Check that the other two inputs (tf, zpk) will work as well
+        tfin = ([1.0], [1.0, 1.0], 0.5)
+        yout_tfimpulse = np.asarray([0.0, 1.0, -1.0])
+        tout, yout = dimpulse(tfin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        zpkin = tf2zpk(tfin[0], tfin[1]) + (0.5,)
+        tout, yout = dimpulse(zpkin, n=3)
+        assert_equal(len(yout), 1)
+        assert_array_almost_equal(yout[0].flatten(), yout_tfimpulse)
+
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dimpulse, system)
+
+    def test_dlsim_trivial(self):
+        a = np.array([[0.0]])
+        b = np.array([[0.0]])
+        c = np.array([[0.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u)
+        assert_array_equal(tout, np.arange(float(n)))
+        assert_array_equal(yout, np.zeros((n, 1)))
+        assert_array_equal(xout, np.zeros((n, 1)))
+
+    def test_dlsim_simple1d(self):
+        a = np.array([[0.5]])
+        b = np.array([[0.0]])
+        c = np.array([[1.0]])
+        d = np.array([[0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        assert_array_equal(tout, np.arange(float(n)))
+        expected = (0.5 ** np.arange(float(n))).reshape(-1, 1)
+        assert_array_equal(yout, expected)
+        assert_array_equal(xout, expected)
+
+    def test_dlsim_simple2d(self):
+        lambda1 = 0.5
+        lambda2 = 0.25
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[0.0],
+                      [0.0]])
+        c = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        d = np.array([[0.0],
+                      [0.0]])
+        n = 5
+        u = np.zeros(n).reshape(-1, 1)
+        tout, yout, xout = dlsim((a, b, c, d, 1), u, x0=1)
+        assert_array_equal(tout, np.arange(float(n)))
+        # The analytical solution:
+        expected = (np.array([lambda1, lambda2]) **
+                                np.arange(float(n)).reshape(-1, 1))
+        assert_array_equal(yout, expected)
+        assert_array_equal(xout, expected)
+
+    def test_more_step_and_impulse(self):
+        lambda1 = 0.5
+        lambda2 = 0.75
+        a = np.array([[lambda1, 0.0],
+                      [0.0, lambda2]])
+        b = np.array([[1.0, 0.0],
+                      [0.0, 1.0]])
+        c = np.array([[1.0, 1.0]])
+        d = np.array([[0.0, 0.0]])
+
+        n = 10
+
+        # Check a step response.
+        ts, ys = dstep((a, b, c, d, 1), n=n)
+
+        # Create the exact step response.
+        stp0 = (1.0 / (1 - lambda1)) * (1.0 - lambda1 ** np.arange(n))
+        stp1 = (1.0 / (1 - lambda2)) * (1.0 - lambda2 ** np.arange(n))
+
+        assert_allclose(ys[0][:, 0], stp0)
+        assert_allclose(ys[1][:, 0], stp1)
+
+        # Check an impulse response with an initial condition.
+        x0 = np.array([1.0, 1.0])
+        ti, yi = dimpulse((a, b, c, d, 1), n=n, x0=x0)
+
+        # Create the exact impulse response.
+        imp = (np.array([lambda1, lambda2]) **
+                            np.arange(-1, n + 1).reshape(-1, 1))
+        imp[0, :] = 0.0
+        # Analytical solution to impulse response
+        y0 = imp[:n, 0] + np.dot(imp[1:n + 1, :], x0)
+        y1 = imp[:n, 1] + np.dot(imp[1:n + 1, :], x0)
+
+        assert_allclose(yi[0][:, 0], y0)
+        assert_allclose(yi[1][:, 0], y1)
+
+        # Check that dt=0.1, n=3 gives 3 time values.
+        system = ([1.0], [1.0, -0.5], 0.1)
+        t, (y,) = dstep(system, n=3)
+        assert_allclose(t, [0, 0.1, 0.2])
+        assert_array_equal(y.T, [[0, 1.0, 1.5]])
+        t, (y,) = dimpulse(system, n=3)
+        assert_allclose(t, [0, 0.1, 0.2])
+        assert_array_equal(y.T, [[0, 1, 0.5]])
+
+
+class TestDlti(object):
+    def test_dlti_instantiation(self):
+        # Test that lti can be instantiated.
+
+        dt = 0.05
+        # TransferFunction
+        s = dlti([1], [-1], dt=dt)
+        assert_(isinstance(s, TransferFunction))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # ZerosPolesGain
+        s = dlti(np.array([]), np.array([-1]), 1, dt=dt)
+        assert_(isinstance(s, ZerosPolesGain))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # StateSpace
+        s = dlti([1], [-1], 1, 3, dt=dt)
+        assert_(isinstance(s, StateSpace))
+        assert_(isinstance(s, dlti))
+        assert_(not isinstance(s, lti))
+        assert_equal(s.dt, dt)
+
+        # Number of inputs
+        assert_raises(ValueError, dlti, 1)
+        assert_raises(ValueError, dlti, 1, 1, 1, 1, 1)
+
+
+class TestStateSpaceDisc(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        StateSpace(1, 1, 1, 1, dt=dt)
+        StateSpace([1], [2], [3], [4], dt=dt)
+        StateSpace(np.array([[1, 2], [3, 4]]), np.array([[1], [2]]),
+                   np.array([[1, 0]]), np.array([[0]]), dt=dt)
+        StateSpace(1, 1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = StateSpace(1, 2, 3, 4, dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(StateSpace(s) is not s)
+        assert_(s.to_ss() is not s)
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_tf() and to_zpk()
+
+        # Getters
+        s = StateSpace(1, 1, 1, 1, dt=0.05)
+        assert_equal(s.poles, [1])
+        assert_equal(s.zeros, [0])
+
+
+class TestTransferFunction(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        TransferFunction(1, 1, dt=dt)
+        TransferFunction([1], [2], dt=dt)
+        TransferFunction(np.array([1]), np.array([2]), dt=dt)
+        TransferFunction(1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(TransferFunction(s) is not s)
+        assert_(s.to_tf() is not s)
+
+    def test_properties(self):
+        # Test setters/getters for cross class properties.
+        # This implicitly tests to_ss() and to_zpk()
+
+        # Getters
+        s = TransferFunction([1, 0], [1, -1], dt=0.05)
+        assert_equal(s.poles, [1])
+        assert_equal(s.zeros, [0])
+
+
+class TestZerosPolesGain(object):
+    def test_initialization(self):
+        # Check that all initializations work
+        dt = 0.05
+        ZerosPolesGain(1, 1, 1, dt=dt)
+        ZerosPolesGain([1], [2], 1, dt=dt)
+        ZerosPolesGain(np.array([1]), np.array([2]), 1, dt=dt)
+        ZerosPolesGain(1, 1, 1, dt=True)
+
+    def test_conversion(self):
+        # Check the conversion functions
+        s = ZerosPolesGain(1, 2, 3, dt=0.05)
+        assert_(isinstance(s.to_ss(), StateSpace))
+        assert_(isinstance(s.to_tf(), TransferFunction))
+        assert_(isinstance(s.to_zpk(), ZerosPolesGain))
+
+        # Make sure copies work
+        assert_(ZerosPolesGain(s) is not s)
+        assert_(s.to_zpk() is not s)
+
+
+class Test_dfreqresp(object):
+
+    def test_manual(self):
+        # Test dfreqresp() real part calculation (manual sanity check).
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10]
+        w, H = dfreqresp(system, w=w)
+
+        # test real
+        expected_re = [1.2383, 0.4130, -0.7553]
+        assert_almost_equal(H.real, expected_re, decimal=4)
+
+        # test imag
+        expected_im = [-0.1555, -1.0214, 0.3955]
+        assert_almost_equal(H.imag, expected_im, decimal=4)
+
+    def test_auto(self):
+        # Test dfreqresp() real part calculation.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        w = [0.1, 1, 10, 100]
+        w, H = dfreqresp(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # test real
+        expected_re = y.real
+        assert_almost_equal(H.real, expected_re)
+
+        # test imag
+        expected_im = y.imag
+        assert_almost_equal(H.imag, expected_im)
+
+    def test_freq_range(self):
+        # Test that freqresp() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(z) = 1 / (z - 0.2),
+        # Expected range is from 0.01 to 10.
+        system = TransferFunction(1, [1, -0.2], dt=0.1)
+        n = 10
+        expected_w = np.linspace(0, np.pi, 10, endpoint=False)
+        w, H = dfreqresp(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, message="divide by zero")
+            sup.filter(RuntimeWarning, message="invalid value encountered")
+            w, H = dfreqresp(system, n=2)
+        assert_equal(w[0], 0.)  # a fail would give not-a-number
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dfreqresp, system)
+
+    def test_from_state_space(self):
+        # H(z) = 2 / z^3 - 0.5 * z^2
+
+        system_TF = dlti([2], [1, -0.5, 0, 0])
+
+        A = np.array([[0.5, 0, 0],
+                      [1, 0, 0],
+                      [0, 1, 0]])
+        B = np.array([[1, 0, 0]]).T
+        C = np.array([[0, 0, 2]])
+        D = 0
+
+        system_SS = dlti(A, B, C, D)
+        w = 10.0**np.arange(-3,0,.5)
+        with suppress_warnings() as sup:
+            sup.filter(BadCoefficients)
+            w1, H1 = dfreqresp(system_TF, w=w)
+            w2, H2 = dfreqresp(system_SS, w=w)
+
+        assert_almost_equal(H1, H2)
+
+    def test_from_zpk(self):
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system_ZPK = dlti([],[0.2],0.3)
+        system_TF = dlti(0.3, [1, -0.2])
+        w = [0.1, 1, 10, 100]
+        w1, H1 = dfreqresp(system_ZPK, w=w)
+        w2, H2 = dfreqresp(system_TF, w=w)
+        assert_almost_equal(H1, H2)
+
+
+class Test_bode(object):
+
+    def test_manual(self):
+        # Test bode() magnitude calculation (manual sanity check).
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=dt)
+        w = [0.1, 0.5, 1, np.pi]
+        w2, mag, phase = dbode(system, w=w)
+
+        # Test mag
+        expected_mag = [-8.5329, -8.8396, -9.6162, -12.0412]
+        assert_almost_equal(mag, expected_mag, decimal=4)
+
+        # Test phase
+        expected_phase = [-7.1575, -35.2814, -67.9809, -180.0000]
+        assert_almost_equal(phase, expected_phase, decimal=4)
+
+        # Test frequency
+        assert_equal(np.array(w) / dt, w2)
+
+    def test_auto(self):
+        # Test bode() magnitude calculation.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        w = np.array([0.1, 0.5, 1, np.pi])
+        w2, mag, phase = dbode(system, w=w)
+        jw = np.exp(w * 1j)
+        y = np.polyval(system.num, jw) / np.polyval(system.den, jw)
+
+        # Test mag
+        expected_mag = 20.0 * np.log10(abs(y))
+        assert_almost_equal(mag, expected_mag)
+
+        # Test phase
+        expected_phase = np.rad2deg(np.angle(y))
+        assert_almost_equal(phase, expected_phase)
+
+    def test_range(self):
+        # Test that bode() finds a reasonable frequency range.
+        # 1st order low-pass filter: H(s) = 0.3 / (z - 0.2),
+        dt = 0.1
+        system = TransferFunction(0.3, [1, -0.2], dt=0.1)
+        n = 10
+        # Expected range is from 0.01 to 10.
+        expected_w = np.linspace(0, np.pi, n, endpoint=False) / dt
+        w, mag, phase = dbode(system, n=n)
+        assert_almost_equal(w, expected_w)
+
+    def test_pole_one(self):
+        # Test that freqresp() doesn't fail on a system with a pole at 0.
+        # integrator, pole at zero: H(s) = 1 / s
+        system = TransferFunction([1], [1, -1], dt=0.1)
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning, message="divide by zero")
+            sup.filter(RuntimeWarning, message="invalid value encountered")
+            w, mag, phase = dbode(system, n=2)
+        assert_equal(w[0], 0.)  # a fail would give not-a-number
+
+    def test_imaginary(self):
+        # bode() should not fail on a system with pure imaginary poles.
+        # The test passes if bode doesn't raise an exception.
+        system = TransferFunction([1], [1, 0, 100], dt=0.1)
+        dbode(system, n=2)
+
+    def test_error(self):
+        # Raise an error for continuous-time systems
+        system = lti([1], [1, 1])
+        assert_raises(AttributeError, dbode, system)
+
+
+class TestTransferFunctionZConversion(object):
+    """Test private conversions between 'z' and 'z**-1' polynomials."""
+
+    def test_full(self):
+        # Numerator and denominator same order
+        num = [2, 3, 4]
+        den = [5, 6, 7]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal(num, num2)
+        assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal(num, num2)
+        assert_equal(den, den2)
+
+    def test_numerator(self):
+        # Numerator lower order than denominator
+        num = [2, 3]
+        den = [5, 6, 7]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal([0, 2, 3], num2)
+        assert_equal(den, den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal([2, 3, 0], num2)
+        assert_equal(den, den2)
+
+    def test_denominator(self):
+        # Numerator higher order than denominator
+        num = [2, 3, 4]
+        den = [5, 6]
+        num2, den2 = TransferFunction._z_to_zinv(num, den)
+        assert_equal(num, num2)
+        assert_equal([0, 5, 6], den2)
+
+        num2, den2 = TransferFunction._zinv_to_z(num, den)
+        assert_equal(num, num2)
+        assert_equal([5, 6, 0], den2)
+

venv/Lib/site-packages/scipy/signal/tests/test_fir_filter_design.py

@@ -0,0 +1,641 @@
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_array_almost_equal,
+                           assert_equal, assert_,
+                           assert_allclose, assert_warns)
+from pytest import raises as assert_raises
+import pytest
+
+from scipy.fft import fft
+from scipy.special import sinc
+from scipy.signal import kaiser_beta, kaiser_atten, kaiserord, \
+    firwin, firwin2, freqz, remez, firls, minimum_phase
+
+
+def test_kaiser_beta():
+    b = kaiser_beta(58.7)
+    assert_almost_equal(b, 0.1102 * 50.0)
+    b = kaiser_beta(22.0)
+    assert_almost_equal(b, 0.5842 + 0.07886)
+    b = kaiser_beta(21.0)
+    assert_equal(b, 0.0)
+    b = kaiser_beta(10.0)
+    assert_equal(b, 0.0)
+
+
+def test_kaiser_atten():
+    a = kaiser_atten(1, 1.0)
+    assert_equal(a, 7.95)
+    a = kaiser_atten(2, 1/np.pi)
+    assert_equal(a, 2.285 + 7.95)
+
+
+def test_kaiserord():
+    assert_raises(ValueError, kaiserord, 1.0, 1.0)
+    numtaps, beta = kaiserord(2.285 + 7.95 - 0.001, 1/np.pi)
+    assert_equal((numtaps, beta), (2, 0.0))
+
+
+class TestFirwin(object):
+
+    def check_response(self, h, expected_response, tol=.05):
+        N = len(h)
+        alpha = 0.5 * (N-1)
+        m = np.arange(0,N) - alpha   # time indices of taps
+        for freq, expected in expected_response:
+            actual = abs(np.sum(h*np.exp(-1.j*np.pi*m*freq)))
+            mse = abs(actual-expected)**2
+            assert_(mse < tol, 'response not as expected, mse=%g > %g'
+               % (mse, tol))
+
+    def test_response(self):
+        N = 51
+        f = .5
+        # increase length just to try even/odd
+        h = firwin(N, f)  # low-pass from 0 to f
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+1, f, window='nuttall')  # specific window
+        self.check_response(h, [(.25,1), (.75,0)])
+
+        h = firwin(N+2, f, pass_zero=False)  # stop from 0 to f --> high-pass
+        self.check_response(h, [(.25,0), (.75,1)])
+
+        f1, f2, f3, f4 = .2, .4, .6, .8
+        h = firwin(N+3, [f1, f2], pass_zero=False)  # band-pass filter
+        self.check_response(h, [(.1,0), (.3,1), (.5,0)])
+
+        h = firwin(N+4, [f1, f2])  # band-stop filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1)])
+
+        h = firwin(N+5, [f1, f2, f3, f4], pass_zero=False, scale=False)
+        self.check_response(h, [(.1,0), (.3,1), (.5,0), (.7,1), (.9,0)])
+
+        h = firwin(N+6, [f1, f2, f3, f4])  # multiband filter
+        self.check_response(h, [(.1,1), (.3,0), (.5,1), (.7,0), (.9,1)])
+
+        h = firwin(N+7, 0.1, width=.03)  # low-pass
+        self.check_response(h, [(.05,1), (.75,0)])
+
+        h = firwin(N+8, 0.1, pass_zero=False)  # high-pass
+        self.check_response(h, [(.05,0), (.75,1)])
+
+    def mse(self, h, bands):
+        """Compute mean squared error versus ideal response across frequency
+        band.
+          h -- coefficients
+          bands -- list of (left, right) tuples relative to 1==Nyquist of
+            passbands
+        """
+        w, H = freqz(h, worN=1024)
+        f = w/np.pi
+        passIndicator = np.zeros(len(w), bool)
+        for left, right in bands:
+            passIndicator |= (f >= left) & (f < right)
+        Hideal = np.where(passIndicator, 1, 0)
+        mse = np.mean(abs(abs(H)-Hideal)**2)
+        return mse
+
+    def test_scaling(self):
+        """
+        For one lowpass, bandpass, and highpass example filter, this test
+        checks two things:
+          - the mean squared error over the frequency domain of the unscaled
+            filter is smaller than the scaled filter (true for rectangular
+            window)
+          - the response of the scaled filter is exactly unity at the center
+            of the first passband
+        """
+        N = 11
+        cases = [
+            ([.5], True, (0, 1)),
+            ([0.2, .6], False, (.4, 1)),
+            ([.5], False, (1, 1)),
+        ]
+        for cutoff, pass_zero, expected_response in cases:
+            h = firwin(N, cutoff, scale=False, pass_zero=pass_zero, window='ones')
+            hs = firwin(N, cutoff, scale=True, pass_zero=pass_zero, window='ones')
+            if len(cutoff) == 1:
+                if pass_zero:
+                    cutoff = [0] + cutoff
+                else:
+                    cutoff = cutoff + [1]
+            assert_(self.mse(h, [cutoff]) < self.mse(hs, [cutoff]),
+                'least squares violation')
+            self.check_response(hs, [expected_response], 1e-12)
+
+
+class TestFirWinMore(object):
+    """Different author, different style, different tests..."""
+
+    def test_lowpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=0.5, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                    [1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='lowpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_highpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+
+        # Ensure that ntaps is odd.
+        ntaps |= 1
+
+        kwargs = dict(cutoff=0.5, window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                    [0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='highpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_bandpass(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=[0.3, 0.7], window=('kaiser', beta), scale=False)
+        taps = firwin(ntaps, pass_zero=False, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.2, 0.3-width/2, 0.3+width/2, 0.5,
+                                0.7-width/2, 0.7+width/2, 0.8, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='bandpass', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_bandstop_multi(self):
+        width = 0.04
+        ntaps, beta = kaiserord(120, width)
+        kwargs = dict(cutoff=[0.2, 0.5, 0.8], window=('kaiser', beta),
+                      scale=False)
+        taps = firwin(ntaps, **kwargs)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 0.1, 0.2-width/2, 0.2+width/2, 0.35,
+                                0.5-width/2, 0.5+width/2, 0.65,
+                                0.8-width/2, 0.8+width/2, 0.9, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                [1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0],
+                decimal=5)
+
+        taps_str = firwin(ntaps, pass_zero='bandstop', **kwargs)
+        assert_allclose(taps, taps_str)
+
+    def test_fs_nyq(self):
+        """Test the fs and nyq keywords."""
+        nyquist = 1000
+        width = 40.0
+        relative_width = width/nyquist
+        ntaps, beta = kaiserord(120, relative_width)
+        taps = firwin(ntaps, cutoff=[300, 700], window=('kaiser', beta),
+                        pass_zero=False, scale=False, fs=2*nyquist)
+
+        # Check the symmetry of taps.
+        assert_array_almost_equal(taps[:ntaps//2], taps[ntaps:ntaps-ntaps//2-1:-1])
+
+        # Check the gain at a few samples where we know it should be approximately 0 or 1.
+        freq_samples = np.array([0.0, 200, 300-width/2, 300+width/2, 500,
+                                700-width/2, 700+width/2, 800, 1000])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples/nyquist)
+        assert_array_almost_equal(np.abs(response),
+                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0], decimal=5)
+
+        taps2 = firwin(ntaps, cutoff=[300, 700], window=('kaiser', beta),
+                        pass_zero=False, scale=False, nyq=nyquist)
+        assert_allclose(taps2, taps)
+
+    def test_bad_cutoff(self):
+        """Test that invalid cutoff argument raises ValueError."""
+        # cutoff values must be greater than 0 and less than 1.
+        assert_raises(ValueError, firwin, 99, -0.5)
+        assert_raises(ValueError, firwin, 99, 1.5)
+        # Don't allow 0 or 1 in cutoff.
+        assert_raises(ValueError, firwin, 99, [0, 0.5])
+        assert_raises(ValueError, firwin, 99, [0.5, 1])
+        # cutoff values must be strictly increasing.
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.2])
+        assert_raises(ValueError, firwin, 99, [0.1, 0.5, 0.5])
+        # Must have at least one cutoff value.
+        assert_raises(ValueError, firwin, 99, [])
+        # 2D array not allowed.
+        assert_raises(ValueError, firwin, 99, [[0.1, 0.2],[0.3, 0.4]])
+        # cutoff values must be less than nyq.
+        assert_raises(ValueError, firwin, 99, 50.0, nyq=40)
+        assert_raises(ValueError, firwin, 99, [10, 20, 30], nyq=25)
+        assert_raises(ValueError, firwin, 99, 50.0, fs=80)
+        assert_raises(ValueError, firwin, 99, [10, 20, 30], fs=50)
+
+    def test_even_highpass_raises_value_error(self):
+        """Test that attempt to create a highpass filter with an even number
+        of taps raises a ValueError exception."""
+        assert_raises(ValueError, firwin, 40, 0.5, pass_zero=False)
+        assert_raises(ValueError, firwin, 40, [.25, 0.5])
+
+    def test_bad_pass_zero(self):
+        """Test degenerate pass_zero cases."""
+        with assert_raises(ValueError, match='pass_zero must be'):
+            firwin(41, 0.5, pass_zero='foo')
+        with assert_raises(TypeError, match='cannot be interpreted'):
+            firwin(41, 0.5, pass_zero=1.)
+        for pass_zero in ('lowpass', 'highpass'):
+            with assert_raises(ValueError, match='cutoff must have one'):
+                firwin(41, [0.5, 0.6], pass_zero=pass_zero)
+        for pass_zero in ('bandpass', 'bandstop'):
+            with assert_raises(ValueError, match='must have at least two'):
+                firwin(41, [0.5], pass_zero=pass_zero)
+
+
+class TestFirwin2(object):
+
+    def test_invalid_args(self):
+        # `freq` and `gain` have different lengths.
+        with assert_raises(ValueError, match='must be of same length'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0])
+        # `nfreqs` is less than `ntaps`.
+        with assert_raises(ValueError, match='ntaps must be less than nfreqs'):
+            firwin2(50, [0, 0.5, 1], [0.0, 1.0, 1.0], nfreqs=33)
+        # Decreasing value in `freq`
+        with assert_raises(ValueError, match='must be nondecreasing'):
+            firwin2(50, [0, 0.5, 0.4, 1.0], [0, .25, .5, 1.0])
+        # Value in `freq` repeated more than once.
+        with assert_raises(ValueError, match='must not occur more than twice'):
+            firwin2(50, [0, .1, .1, .1, 1.0], [0.0, 0.5, 0.75, 1.0, 1.0])
+        # `freq` does not start at 0.0.
+        with assert_raises(ValueError, match='start with 0'):
+            firwin2(50, [0.5, 1.0], [0.0, 1.0])
+        # `freq` does not end at fs/2.
+        with assert_raises(ValueError, match='end with fs/2'):
+            firwin2(50, [0.0, 0.5], [0.0, 1.0])
+        # Value 0 is repeated in `freq`
+        with assert_raises(ValueError, match='0 must not be repeated'):
+            firwin2(50, [0.0, 0.0, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value fs/2 is repeated in `freq`
+        with assert_raises(ValueError, match='fs/2 must not be repeated'):
+            firwin2(50, [0.0, 0.5, 1.0, 1.0], [1.0, 1.0, 0.0, 0.0])
+        # Value in `freq` that is too close to a repeated number
+        with assert_raises(ValueError, match='cannot contain numbers '
+                                             'that are too close'):
+            firwin2(50, [0.0, 0.5 - np.finfo(float).eps * 0.5, 0.5, 0.5, 1.0],
+                        [1.0, 1.0, 1.0, 0.0, 0.0])
+
+        # Type II filter, but the gain at nyquist frequency is not zero.
+        with assert_raises(ValueError, match='Type II filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0])
+
+        # Type III filter, but the gains at nyquist and zero rate are not zero.
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [0.0, 1.0, 1.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+        with assert_raises(ValueError, match='Type III filter'):
+            firwin2(17, [0.0, 0.5, 1.0], [1.0, 1.0, 1.0], antisymmetric=True)
+
+        # Type IV filter, but the gain at zero rate is not zero.
+        with assert_raises(ValueError, match='Type IV filter'):
+            firwin2(16, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0], antisymmetric=True)
+
+    def test01(self):
+        width = 0.04
+        beta = 12.0
+        ntaps = 400
+        # Filter is 1 from w=0 to w=0.5, then decreases linearly from 1 to 0 as w
+        # increases from w=0.5 to w=1  (w=1 is the Nyquist frequency).
+        freq = [0.0, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.25, 0.5-width/2, 0.5+width/2,
+                                                        0.75, 1.0-width/2])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                        [1.0, 1.0, 1.0, 1.0-width, 0.5, width], decimal=5)
+
+    def test02(self):
+        width = 0.04
+        beta = 12.0
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = 401
+        # An ideal highpass filter.
+        freq = [0.0, 0.5, 0.5, 1.0]
+        gain = [0.0, 0.0, 1.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.25, 0.5-width, 0.5+width, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                                [0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+    def test03(self):
+        width = 0.02
+        ntaps, beta = kaiserord(120, width)
+        # ntaps must be odd for positive gain at Nyquist.
+        ntaps = int(ntaps) | 1
+        freq = [0.0, 0.4, 0.4, 0.5, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0, 0.0, 1.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=('kaiser', beta))
+        freq_samples = np.array([0.0, 0.4-width, 0.4+width, 0.45,
+                                    0.5-width, 0.5+width, 0.75, 1.0])
+        freqs, response = freqz(taps, worN=np.pi*freq_samples)
+        assert_array_almost_equal(np.abs(response),
+                    [1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0], decimal=5)
+
+    def test04(self):
+        """Test firwin2 when window=None."""
+        ntaps = 5
+        # Ideal lowpass: gain is 1 on [0,0.5], and 0 on [0.5, 1.0]
+        freq = [0.0, 0.5, 0.5, 1.0]
+        gain = [1.0, 1.0, 0.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=None, nfreqs=8193)
+        alpha = 0.5 * (ntaps - 1)
+        m = np.arange(0, ntaps) - alpha
+        h = 0.5 * sinc(0.5 * m)
+        assert_array_almost_equal(h, taps)
+
+    def test05(self):
+        """Test firwin2 for calculating Type IV filters"""
+        ntaps = 1500
+
+        freq = [0.0, 1.0]
+        gain = [0.0, 1.0]
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+        assert_array_almost_equal(taps[: ntaps // 2], -taps[ntaps // 2:][::-1])
+
+        freqs, response = freqz(taps, worN=2048)
+        assert_array_almost_equal(abs(response), freqs / np.pi, decimal=4)
+
+    def test06(self):
+        """Test firwin2 for calculating Type III filters"""
+        ntaps = 1501
+
+        freq = [0.0, 0.5, 0.55, 1.0]
+        gain = [0.0, 0.5, 0.0, 0.0]
+        taps = firwin2(ntaps, freq, gain, window=None, antisymmetric=True)
+        assert_equal(taps[ntaps // 2], 0.0)
+        assert_array_almost_equal(taps[: ntaps // 2], -taps[ntaps // 2 + 1:][::-1])
+
+        freqs, response1 = freqz(taps, worN=2048)
+        response2 = np.interp(freqs / np.pi, freq, gain)
+        assert_array_almost_equal(abs(response1), response2, decimal=3)
+
+    def test_fs_nyq(self):
+        taps1 = firwin2(80, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0])
+        taps2 = firwin2(80, [0.0, 30.0, 60.0], [1.0, 1.0, 0.0], fs=120.0)
+        assert_array_almost_equal(taps1, taps2)
+        taps2 = firwin2(80, [0.0, 30.0, 60.0], [1.0, 1.0, 0.0], nyq=60.0)
+        assert_array_almost_equal(taps1, taps2)
+
+    def test_tuple(self):
+        taps1 = firwin2(150, (0.0, 0.5, 0.5, 1.0), (1.0, 1.0, 0.0, 0.0))
+        taps2 = firwin2(150, [0.0, 0.5, 0.5, 1.0], [1.0, 1.0, 0.0, 0.0])
+        assert_array_almost_equal(taps1, taps2)
+
+    def test_input_modyfication(self):
+        freq1 = np.array([0.0, 0.5, 0.5, 1.0])
+        freq2 = np.array(freq1)
+        firwin2(80, freq1, [1.0, 1.0, 0.0, 0.0])
+        assert_equal(freq1, freq2)
+
+
+class TestRemez(object):
+
+    def test_bad_args(self):
+        assert_raises(ValueError, remez, 11, [0.1, 0.4], [1], type='pooka')
+
+    def test_hilbert(self):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design an unity gain hilbert bandpass filter from w to 0.5-w
+        h = remez(11, [a, 0.5-a], [1], type='hilbert')
+
+        # make sure the filter has correct # of taps
+        assert_(len(h) == N, "Number of Taps")
+
+        # make sure it is type III (anti-symmetric tap coefficients)
+        assert_array_almost_equal(h[:(N-1)//2], -h[:-(N-1)//2-1:-1])
+
+        # Since the requested response is symmetric, all even coefficients
+        # should be zero (or in this case really small)
+        assert_((abs(h[1::2]) < 1e-15).all(), "Even Coefficients Equal Zero")
+
+        # now check the frequency response
+        w, H = freqz(h, 1)
+        f = w/2/np.pi
+        Hmag = abs(H)
+
+        # should have a zero at 0 and pi (in this case close to zero)
+        assert_((Hmag[[0, -1]] < 0.02).all(), "Zero at zero and pi")
+
+        # check that the pass band is close to unity
+        idx = np.logical_and(f > a, f < 0.5-a)
+        assert_((abs(Hmag[idx] - 1) < 0.015).all(), "Pass Band Close To Unity")
+
+    def test_compare(self):
+        # test comparison to MATLAB
+        k = [0.024590270518440, -0.041314581814658, -0.075943803756711,
+             -0.003530911231040, 0.193140296954975, 0.373400753484939,
+             0.373400753484939, 0.193140296954975, -0.003530911231040,
+             -0.075943803756711, -0.041314581814658, 0.024590270518440]
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], Hz=2.)
+        assert_allclose(h, k)
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], fs=2.)
+        assert_allclose(h, k)
+
+        h = [-0.038976016082299, 0.018704846485491, -0.014644062687875,
+             0.002879152556419, 0.016849978528150, -0.043276706138248,
+             0.073641298245579, -0.103908158578635, 0.129770906801075,
+             -0.147163447297124, 0.153302248456347, -0.147163447297124,
+             0.129770906801075, -0.103908158578635, 0.073641298245579,
+             -0.043276706138248, 0.016849978528150, 0.002879152556419,
+             -0.014644062687875, 0.018704846485491, -0.038976016082299]
+        assert_allclose(remez(21, [0, 0.8, 0.9, 1], [0, 1], Hz=2.), h)
+        assert_allclose(remez(21, [0, 0.8, 0.9, 1], [0, 1], fs=2.), h)
+
+
+class TestFirls(object):
+
+    def test_bad_args(self):
+        # even numtaps
+        assert_raises(ValueError, firls, 10, [0.1, 0.2], [0, 0])
+        # odd bands
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.4], [0, 0, 0])
+        # len(bands) != len(desired)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.4], [0, 0, 0])
+        # non-monotonic bands
+        assert_raises(ValueError, firls, 11, [0.2, 0.1], [0, 0])
+        assert_raises(ValueError, firls, 11, [0.1, 0.2, 0.3, 0.3], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.3, 0.4, 0.1, 0.2], [0] * 4)
+        assert_raises(ValueError, firls, 11, [0.1, 0.3, 0.2, 0.4], [0] * 4)
+        # negative desired
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [-1, 1])
+        # len(weight) != len(pairs)
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], [1, 2])
+        # negative weight
+        assert_raises(ValueError, firls, 11, [0.1, 0.2], [0, 0], [-1])
+
+    def test_firls(self):
+        N = 11  # number of taps in the filter
+        a = 0.1  # width of the transition band
+
+        # design a halfband symmetric low-pass filter
+        h = firls(11, [0, a, 0.5-a, 0.5], [1, 1, 0, 0], fs=1.0)
+
+        # make sure the filter has correct # of taps
+        assert_equal(len(h), N)
+
+        # make sure it is symmetric
+        midx = (N-1) // 2
+        assert_array_almost_equal(h[:midx], h[:-midx-1:-1])
+
+        # make sure the center tap is 0.5
+        assert_almost_equal(h[midx], 0.5)
+
+        # For halfband symmetric, odd coefficients (except the center)
+        # should be zero (really small)
+        hodd = np.hstack((h[1:midx:2], h[-midx+1::2]))
+        assert_array_almost_equal(hodd, 0)
+
+        # now check the frequency response
+        w, H = freqz(h, 1)
+        f = w/2/np.pi
+        Hmag = np.abs(H)
+
+        # check that the pass band is close to unity
+        idx = np.logical_and(f > 0, f < a)
+        assert_array_almost_equal(Hmag[idx], 1, decimal=3)
+
+        # check that the stop band is close to zero
+        idx = np.logical_and(f > 0.5-a, f < 0.5)
+        assert_array_almost_equal(Hmag[idx], 0, decimal=3)
+
+    def test_compare(self):
+        # compare to OCTAVE output
+        taps = firls(9, [0, 0.5, 0.55, 1], [1, 1, 0, 0], [1, 2])
+        # >> taps = firls(8, [0 0.5 0.55 1], [1 1 0 0], [1, 2]);
+        known_taps = [-6.26930101730182e-04, -1.03354450635036e-01,
+                      -9.81576747564301e-03, 3.17271686090449e-01,
+                      5.11409425599933e-01, 3.17271686090449e-01,
+                      -9.81576747564301e-03, -1.03354450635036e-01,
+                      -6.26930101730182e-04]
+        assert_allclose(taps, known_taps)
+
+        # compare to MATLAB output
+        taps = firls(11, [0, 0.5, 0.5, 1], [1, 1, 0, 0], [1, 2])
+        # >> taps = firls(10, [0 0.5 0.5 1], [1 1 0 0], [1, 2]);
+        known_taps = [
+            0.058545300496815, -0.014233383714318, -0.104688258464392,
+            0.012403323025279, 0.317930861136062, 0.488047220029700,
+            0.317930861136062, 0.012403323025279, -0.104688258464392,
+            -0.014233383714318, 0.058545300496815]
+        assert_allclose(taps, known_taps)
+
+        # With linear changes:
+        taps = firls(7, (0, 1, 2, 3, 4, 5), [1, 0, 0, 1, 1, 0], fs=20)
+        # >> taps = firls(6, [0, 0.1, 0.2, 0.3, 0.4, 0.5], [1, 0, 0, 1, 1, 0])
+        known_taps = [
+            1.156090832768218, -4.1385894727395849, 7.5288619164321826,
+            -8.5530572592947856, 7.5288619164321826, -4.1385894727395849,
+            1.156090832768218]
+        assert_allclose(taps, known_taps)
+
+        taps = firls(7, (0, 1, 2, 3, 4, 5), [1, 0, 0, 1, 1, 0], nyq=10)
+        assert_allclose(taps, known_taps)
+
+        with pytest.raises(ValueError, match='between 0 and 1'):
+            firls(7, [0, 1], [0, 1], nyq=0.5)
+
+    def test_rank_deficient(self):
+        # solve() runs but warns (only sometimes, so here we don't use match)
+        x = firls(21, [0, 0.1, 0.9, 1], [1, 1, 0, 0])
+        w, h = freqz(x, fs=2.)
+        assert_allclose(np.abs(h[:2]), 1., atol=1e-5)
+        assert_allclose(np.abs(h[-2:]), 0., atol=1e-6)
+        # switch to pinvh (tolerances could be higher with longer
+        # filters, but using shorter ones is faster computationally and
+        # the idea is the same)
+        x = firls(101, [0, 0.01, 0.99, 1], [1, 1, 0, 0])
+        w, h = freqz(x, fs=2.)
+        mask = w < 0.01
+        assert mask.sum() > 3
+        assert_allclose(np.abs(h[mask]), 1., atol=1e-4)
+        mask = w > 0.99
+        assert mask.sum() > 3
+        assert_allclose(np.abs(h[mask]), 0., atol=1e-4)
+
+
+class TestMinimumPhase(object):
+
+    def test_bad_args(self):
+        # not enough taps
+        assert_raises(ValueError, minimum_phase, [1.])
+        assert_raises(ValueError, minimum_phase, [1., 1.])
+        assert_raises(ValueError, minimum_phase, np.full(10, 1j))
+        assert_raises(ValueError, minimum_phase, 'foo')
+        assert_raises(ValueError, minimum_phase, np.ones(10), n_fft=8)
+        assert_raises(ValueError, minimum_phase, np.ones(10), method='foo')
+        assert_warns(RuntimeWarning, minimum_phase, np.arange(3))
+
+    def test_homomorphic(self):
+        # check that it can recover frequency responses of arbitrary
+        # linear-phase filters
+
+        # for some cases we can get the actual filter back
+        h = [1, -1]
+        h_new = minimum_phase(np.convolve(h, h[::-1]))
+        assert_allclose(h_new, h, rtol=0.05)
+
+        # but in general we only guarantee we get the magnitude back
+        rng = np.random.RandomState(0)
+        for n in (2, 3, 10, 11, 15, 16, 17, 20, 21, 100, 101):
+            h = rng.randn(n)
+            h_new = minimum_phase(np.convolve(h, h[::-1]))
+            assert_allclose(np.abs(fft(h_new)),
+                            np.abs(fft(h)), rtol=1e-4)
+
+    def test_hilbert(self):
+        # compare to MATLAB output of reference implementation
+
+        # f=[0 0.3 0.5 1];
+        # a=[1 1 0 0];
+        # h=remez(11,f,a);
+        h = remez(12, [0, 0.3, 0.5, 1], [1, 0], fs=2.)
+        k = [0.349585548646686, 0.373552164395447, 0.326082685363438,
+             0.077152207480935, -0.129943946349364, -0.059355880509749]
+        m = minimum_phase(h, 'hilbert')
+        assert_allclose(m, k, rtol=5e-3)
+
+        # f=[0 0.8 0.9 1];
+        # a=[0 0 1 1];
+        # h=remez(20,f,a);
+        h = remez(21, [0, 0.8, 0.9, 1], [0, 1], fs=2.)
+        k = [0.232486803906329, -0.133551833687071, 0.151871456867244,
+             -0.157957283165866, 0.151739294892963, -0.129293146705090,
+             0.100787844523204, -0.065832656741252, 0.035361328741024,
+             -0.014977068692269, -0.158416139047557]
+        m = minimum_phase(h, 'hilbert', n_fft=2**19)
+        assert_allclose(m, k, rtol=2e-3)

venv/Lib/site-packages/scipy/signal/tests/test_max_len_seq.py

@@ -0,0 +1,65 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_array_equal
+from pytest import raises as assert_raises
+
+from numpy.fft import fft, ifft
+
+from scipy.signal import max_len_seq
+
+
+class TestMLS(object):
+
+    def test_mls_inputs(self):
+        # can't all be zero state
+        assert_raises(ValueError, max_len_seq,
+                      10, state=np.zeros(10))
+        # wrong size state
+        assert_raises(ValueError, max_len_seq, 10,
+                      state=np.ones(3))
+        # wrong length
+        assert_raises(ValueError, max_len_seq, 10, length=-1)
+        assert_array_equal(max_len_seq(10, length=0)[0], [])
+        # unknown taps
+        assert_raises(ValueError, max_len_seq, 64)
+        # bad taps
+        assert_raises(ValueError, max_len_seq, 10, taps=[-1, 1])
+
+    def test_mls_output(self):
+        # define some alternate working taps
+        alt_taps = {2: [1], 3: [2], 4: [3], 5: [4, 3, 2], 6: [5, 4, 1], 7: [4],
+                    8: [7, 5, 3]}
+        # assume the other bit levels work, too slow to test higher orders...
+        for nbits in range(2, 8):
+            for state in [None, np.round(np.random.rand(nbits))]:
+                for taps in [None, alt_taps[nbits]]:
+                    if state is not None and np.all(state == 0):
+                        state[0] = 1  # they can't all be zero
+                    orig_m = max_len_seq(nbits, state=state,
+                                         taps=taps)[0]
+                    m = 2. * orig_m - 1.  # convert to +/- 1 representation
+                    # First, make sure we got all 1's or -1
+                    err_msg = "mls had non binary terms"
+                    assert_array_equal(np.abs(m), np.ones_like(m),
+                                       err_msg=err_msg)
+                    # Test via circular cross-correlation, which is just mult.
+                    # in the frequency domain with one signal conjugated
+                    tester = np.real(ifft(fft(m) * np.conj(fft(m))))
+                    out_len = 2**nbits - 1
+                    # impulse amplitude == test_len
+                    err_msg = "mls impulse has incorrect value"
+                    assert_allclose(tester[0], out_len, err_msg=err_msg)
+                    # steady-state is -1
+                    err_msg = "mls steady-state has incorrect value"
+                    assert_allclose(tester[1:], np.full(out_len - 1, -1),
+                                    err_msg=err_msg)
+                    # let's do the split thing using a couple options
+                    for n in (1, 2**(nbits - 1)):
+                        m1, s1 = max_len_seq(nbits, state=state, taps=taps,
+                                             length=n)
+                        m2, s2 = max_len_seq(nbits, state=s1, taps=taps,
+                                             length=1)
+                        m3, s3 = max_len_seq(nbits, state=s2, taps=taps,
+                                             length=out_len - n - 1)
+                        new_m = np.concatenate((m1, m2, m3))
+                        assert_array_equal(orig_m, new_m)
+

venv/Lib/site-packages/scipy/signal/tests/test_peak_finding.py

@@ -0,0 +1,847 @@
+import copy
+
+import numpy as np
+from numpy.testing import (
+    assert_,
+    assert_equal,
+    assert_allclose,
+    assert_array_equal
+)
+import pytest
+from pytest import raises, warns
+
+from scipy.signal._peak_finding import (
+    argrelmax,
+    argrelmin,
+    peak_prominences,
+    peak_widths,
+    _unpack_condition_args,
+    find_peaks,
+    find_peaks_cwt,
+    _identify_ridge_lines
+)
+from scipy.signal._peak_finding_utils import _local_maxima_1d, PeakPropertyWarning
+
+
+def _gen_gaussians(center_locs, sigmas, total_length):
+    xdata = np.arange(0, total_length).astype(float)
+    out_data = np.zeros(total_length, dtype=float)
+    for ind, sigma in enumerate(sigmas):
+        tmp = (xdata - center_locs[ind]) / sigma
+        out_data += np.exp(-(tmp**2))
+    return out_data
+
+
+def _gen_gaussians_even(sigmas, total_length):
+    num_peaks = len(sigmas)
+    delta = total_length / (num_peaks + 1)
+    center_locs = np.linspace(delta, total_length - delta, num=num_peaks).astype(int)
+    out_data = _gen_gaussians(center_locs, sigmas, total_length)
+    return out_data, center_locs
+
+
+def _gen_ridge_line(start_locs, max_locs, length, distances, gaps):
+    """
+    Generate coordinates for a ridge line.
+
+    Will be a series of coordinates, starting a start_loc (length 2).
+    The maximum distance between any adjacent columns will be
+    `max_distance`, the max distance between adjacent rows
+    will be `map_gap'.
+
+    `max_locs` should be the size of the intended matrix. The
+    ending coordinates are guaranteed to be less than `max_locs`,
+    although they may not approach `max_locs` at all.
+    """
+
+    def keep_bounds(num, max_val):
+        out = max(num, 0)
+        out = min(out, max_val)
+        return out
+
+    gaps = copy.deepcopy(gaps)
+    distances = copy.deepcopy(distances)
+
+    locs = np.zeros([length, 2], dtype=int)
+    locs[0, :] = start_locs
+    total_length = max_locs[0] - start_locs[0] - sum(gaps)
+    if total_length < length:
+        raise ValueError('Cannot generate ridge line according to constraints')
+    dist_int = length / len(distances) - 1
+    gap_int = length / len(gaps) - 1
+    for ind in range(1, length):
+        nextcol = locs[ind - 1, 1]
+        nextrow = locs[ind - 1, 0] + 1
+        if (ind % dist_int == 0) and (len(distances) > 0):
+            nextcol += ((-1)**ind)*distances.pop()
+        if (ind % gap_int == 0) and (len(gaps) > 0):
+            nextrow += gaps.pop()
+        nextrow = keep_bounds(nextrow, max_locs[0])
+        nextcol = keep_bounds(nextcol, max_locs[1])
+        locs[ind, :] = [nextrow, nextcol]
+
+    return [locs[:, 0], locs[:, 1]]
+
+
+class TestLocalMaxima1d(object):
+
+    def test_empty(self):
+        """Test with empty signal."""
+        x = np.array([], dtype=np.float64)
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_linear(self):
+        """Test with linear signal."""
+        x = np.linspace(0, 100)
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_simple(self):
+        """Test with simple signal."""
+        x = np.linspace(-10, 10, 50)
+        x[2::3] += 1
+        expected = np.arange(2, 50, 3)
+        for array in _local_maxima_1d(x):
+            # For plateaus of size 1, the edges are identical with the
+            # midpoints
+            assert_equal(array, expected)
+            assert_(array.base is None)
+
+    def test_flat_maxima(self):
+        """Test if flat maxima are detected correctly."""
+        x = np.array([-1.3, 0, 1, 0, 2, 2, 0, 3, 3, 3, 2.99, 4, 4, 4, 4, -10,
+                      -5, -5, -5, -5, -5, -10])
+        midpoints, left_edges, right_edges = _local_maxima_1d(x)
+        assert_equal(midpoints, np.array([2, 4, 8, 12, 18]))
+        assert_equal(left_edges, np.array([2, 4, 7, 11, 16]))
+        assert_equal(right_edges, np.array([2, 5, 9, 14, 20]))
+
+    @pytest.mark.parametrize('x', [
+        np.array([1., 0, 2]),
+        np.array([3., 3, 0, 4, 4]),
+        np.array([5., 5, 5, 0, 6, 6, 6]),
+    ])
+    def test_signal_edges(self, x):
+        """Test if behavior on signal edges is correct."""
+        for array in _local_maxima_1d(x):
+            assert_equal(array, np.array([]))
+            assert_(array.base is None)
+
+    def test_exceptions(self):
+        """Test input validation and raised exceptions."""
+        with raises(ValueError, match="wrong number of dimensions"):
+            _local_maxima_1d(np.ones((1, 1)))
+        with raises(ValueError, match="expected 'float64_t'"):
+            _local_maxima_1d(np.ones(1, dtype=int))
+        with raises(TypeError, match="list"):
+            _local_maxima_1d([1., 2.])
+        with raises(TypeError, match="'x' must not be None"):
+            _local_maxima_1d(None)
+
+
+class TestRidgeLines(object):
+
+    def test_empty(self):
+        test_matr = np.zeros([20, 100])
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 0)
+
+    def test_minimal(self):
+        test_matr = np.zeros([20, 100])
+        test_matr[0, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 1)
+
+        test_matr = np.zeros([20, 100])
+        test_matr[0:2, 10] = 1
+        lines = _identify_ridge_lines(test_matr, np.full(20, 2), 1)
+        assert_(len(lines) == 1)
+
+    def test_single_pass(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 0, 1]
+        test_matr = np.zeros([20, 50]) + 1e-12
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_distances = np.full(20, max(distances))
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max(gaps) + 1)
+        assert_array_equal(identified_lines, [line])
+
+    def test_single_bigdist(self):
+        distances = [0, 1, 2, 5]
+        gaps = [0, 1, 2, 4]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 3
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the distance is too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max(gaps) + 1)
+        assert_(len(identified_lines) == 2)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggap(self):
+        distances = [0, 1, 2, 5]
+        max_gap = 3
+        gaps = [0, 4, 2, 1]
+        test_matr = np.zeros([20, 50])
+        length = 12
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 6
+        max_distances = np.full(20, max_dist)
+        #This should get 2 lines, since the gap is too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert_(len(identified_lines) == 2)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+    def test_single_biggaps(self):
+        distances = [0]
+        max_gap = 1
+        gaps = [3, 6]
+        test_matr = np.zeros([50, 50])
+        length = 30
+        line = _gen_ridge_line([0, 25], test_matr.shape, length, distances, gaps)
+        test_matr[line[0], line[1]] = 1
+        max_dist = 1
+        max_distances = np.full(50, max_dist)
+        #This should get 3 lines, since the gaps are too large
+        identified_lines = _identify_ridge_lines(test_matr, max_distances, max_gap)
+        assert_(len(identified_lines) == 3)
+
+        for iline in identified_lines:
+            adists = np.diff(iline[1])
+            np.testing.assert_array_less(np.abs(adists), max_dist)
+
+            agaps = np.diff(iline[0])
+            np.testing.assert_array_less(np.abs(agaps), max(gaps) + 0.1)
+
+
+class TestArgrel(object):
+
+    def test_empty(self):
+        # Regression test for gh-2832.
+        # When there are no relative extrema, make sure that
+        # the number of empty arrays returned matches the
+        # dimension of the input.
+
+        empty_array = np.array([], dtype=int)
+
+        z1 = np.zeros(5)
+
+        i = argrelmin(z1)
+        assert_equal(len(i), 1)
+        assert_array_equal(i[0], empty_array)
+
+        z2 = np.zeros((3,5))
+
+        row, col = argrelmin(z2, axis=0)
+        assert_array_equal(row, empty_array)
+        assert_array_equal(col, empty_array)
+
+        row, col = argrelmin(z2, axis=1)
+        assert_array_equal(row, empty_array)
+        assert_array_equal(col, empty_array)
+
+    def test_basic(self):
+        # Note: the docstrings for the argrel{min,max,extrema} functions
+        # do not give a guarantee of the order of the indices, so we'll
+        # sort them before testing.
+
+        x = np.array([[1, 2, 2, 3, 2],
+                      [2, 1, 2, 2, 3],
+                      [3, 2, 1, 2, 2],
+                      [2, 3, 2, 1, 2],
+                      [1, 2, 3, 2, 1]])
+
+        row, col = argrelmax(x, axis=0)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [4, 0, 1])
+
+        row, col = argrelmax(x, axis=1)
+        order = np.argsort(row)
+        assert_equal(row[order], [0, 3, 4])
+        assert_equal(col[order], [3, 1, 2])
+
+        row, col = argrelmin(x, axis=0)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [1, 2, 3])
+
+        row, col = argrelmin(x, axis=1)
+        order = np.argsort(row)
+        assert_equal(row[order], [1, 2, 3])
+        assert_equal(col[order], [1, 2, 3])
+
+    def test_highorder(self):
+        order = 2
+        sigmas = [1.0, 2.0, 10.0, 5.0, 15.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 500)
+        test_data[act_locs + order] = test_data[act_locs]*0.99999
+        test_data[act_locs - order] = test_data[act_locs]*0.99999
+        rel_max_locs = argrelmax(test_data, order=order, mode='clip')[0]
+
+        assert_(len(rel_max_locs) == len(act_locs))
+        assert_((rel_max_locs == act_locs).all())
+
+    def test_2d_gaussians(self):
+        sigmas = [1.0, 2.0, 10.0]
+        test_data, act_locs = _gen_gaussians_even(sigmas, 100)
+        rot_factor = 20
+        rot_range = np.arange(0, len(test_data)) - rot_factor
+        test_data_2 = np.vstack([test_data, test_data[rot_range]])
+        rel_max_rows, rel_max_cols = argrelmax(test_data_2, axis=1, order=1)
+
+        for rw in range(0, test_data_2.shape[0]):
+            inds = (rel_max_rows == rw)
+
+            assert_(len(rel_max_cols[inds]) == len(act_locs))
+            assert_((act_locs == (rel_max_cols[inds] - rot_factor*rw)).all())
+
+
+class TestPeakProminences(object):
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        out = peak_prominences([1, 2, 3], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert_(arr.size == 0)
+            assert_(arr.dtype == dtype)
+
+        out = peak_prominences([], [])
+        for arr, dtype in zip(out, [np.float64, np.intp, np.intp]):
+            assert_(arr.size == 0)
+            assert_(arr.dtype == dtype)
+
+    def test_basic(self):
+        """
+        Test if height of prominences is correctly calculated in signal with
+        rising baseline (peak widths are 1 sample).
+        """
+        # Prepare basic signal
+        x = np.array([-1, 1.2, 1.2, 1, 3.2, 1.3, 2.88, 2.1])
+        peaks = np.array([1, 2, 4, 6])
+        lbases = np.array([0, 0, 0, 5])
+        rbases = np.array([3, 3, 5, 7])
+        proms = x[peaks] - np.max([x[lbases], x[rbases]], axis=0)
+        # Test if calculation matches handcrafted result
+        out = peak_prominences(x, peaks)
+        assert_equal(out[0], proms)
+        assert_equal(out[1], lbases)
+        assert_equal(out[2], rbases)
+
+    def test_edge_cases(self):
+        """
+        Test edge cases.
+        """
+        # Peaks have same height, prominence and bases
+        x = [0, 2, 1, 2, 1, 2, 0]
+        peaks = [1, 3, 5]
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        assert_equal(proms, [2, 2, 2])
+        assert_equal(lbases, [0, 0, 0])
+        assert_equal(rbases, [6, 6, 6])
+
+        # Peaks have same height & prominence but different bases
+        x = [0, 1, 0, 1, 0, 1, 0]
+        peaks = np.array([1, 3, 5])
+        proms, lbases, rbases = peak_prominences(x, peaks)
+        assert_equal(proms, [1, 1, 1])
+        assert_equal(lbases, peaks - 1)
+        assert_equal(rbases, peaks + 1)
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([-9, 9, 9, 0, 3, 1], 2)
+        peaks = np.repeat([1, 2, 4], 2)
+        proms, lbases, rbases = peak_prominences(x[::2], peaks[::2])
+        assert_equal(proms, [9, 9, 2])
+        assert_equal(lbases, [0, 0, 3])
+        assert_equal(rbases, [3, 3, 5])
+
+    def test_wlen(self):
+        """
+        Test if wlen actually shrinks the evaluation range correctly.
+        """
+        x = [0, 1, 2, 3, 1, 0, -1]
+        peak = [3]
+        # Test rounding behavior of wlen
+        assert_equal(peak_prominences(x, peak), [3., 0, 6])
+        for wlen, i in [(8, 0), (7, 0), (6, 0), (5, 1), (3.2, 1), (3, 2), (1.1, 2)]:
+            assert_equal(peak_prominences(x, peak, wlen), [3. - i, 0 + i, 6 - i])
+
+    def test_exceptions(self):
+        """
+        Verify that exceptions and warnings are raised.
+        """
+        # x with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([[0, 1, 1, 0]], [1, 2])
+        # peaks with dimension > 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences([0, 1, 1, 0], [[1, 2]])
+        # x with dimension < 1
+        with raises(ValueError, match='1-D array'):
+            peak_prominences(3, [0,])
+
+        # empty x with supplied
+        with raises(ValueError, match='not a valid index'):
+            peak_prominences([], [0])
+        # invalid indices with non-empty x
+        for p in [-100, -1, 3, 1000]:
+            with raises(ValueError, match='not a valid index'):
+                peak_prominences([1, 0, 2], [p])
+
+        # peaks is not cast-able to np.intp
+        with raises(TypeError, match='cannot safely cast'):
+            peak_prominences([0, 1, 1, 0], [1.1, 2.3])
+
+        # wlen < 3
+        with raises(ValueError, match='wlen'):
+            peak_prominences(np.arange(10), [3, 5], wlen=1)
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a prominence of 0"
+        for p in [0, 1, 2]:
+            with warns(PeakPropertyWarning, match=msg):
+                peak_prominences([1, 0, 2], [p,])
+        with warns(PeakPropertyWarning, match=msg):
+            peak_prominences([0, 1, 1, 1, 0], [2], wlen=2)
+
+
+class TestPeakWidths(object):
+
+    def test_empty(self):
+        """
+        Test if an empty array is returned if no peaks are provided.
+        """
+        widths = peak_widths([], [])[0]
+        assert_(isinstance(widths, np.ndarray))
+        assert_equal(widths.size, 0)
+        widths = peak_widths([1, 2, 3], [])[0]
+        assert_(isinstance(widths, np.ndarray))
+        assert_equal(widths.size, 0)
+        out = peak_widths([], [])
+        for arr in out:
+            assert_(isinstance(arr, np.ndarray))
+            assert_equal(arr.size, 0)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_basic(self):
+        """
+        Test a simple use case with easy to verify results at different relative
+        heights.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1])
+        prominence = 2
+        for rel_height, width_true, lip_true, rip_true in [
+            (0., 0., 3., 3.),  # raises warning
+            (0.25, 1., 2.5, 3.5),
+            (0.5, 2., 2., 4.),
+            (0.75, 3., 1.5, 4.5),
+            (1., 4., 1., 5.),
+            (2., 5., 1., 6.),
+            (3., 5., 1., 6.)
+        ]:
+            width_calc, height, lip_calc, rip_calc = peak_widths(
+                x, [3], rel_height)
+            assert_allclose(width_calc, width_true)
+            assert_allclose(height, 2 - rel_height * prominence)
+            assert_allclose(lip_calc, lip_true)
+            assert_allclose(rip_calc, rip_true)
+
+    def test_non_contiguous(self):
+        """
+        Test with non-C-contiguous input arrays.
+        """
+        x = np.repeat([0, 100, 50], 4)
+        peaks = np.repeat([1], 3)
+        result = peak_widths(x[::4], peaks[::3])
+        assert_equal(result, [0.75, 75, 0.75, 1.5])
+
+    def test_exceptions(self):
+        """
+        Verify that argument validation works as intended.
+        """
+        with raises(ValueError, match='1-D array'):
+            # x with dimension > 1
+            peak_widths(np.zeros((3, 4)), np.ones(3))
+        with raises(ValueError, match='1-D array'):
+            # x with dimension < 1
+            peak_widths(3, [0])
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension > 1
+            peak_widths(np.arange(10), np.ones((3, 2), dtype=np.intp))
+        with raises(ValueError, match='1-D array'):
+            # peaks with dimension < 1
+            peak_widths(np.arange(10), 3)
+        with raises(ValueError, match='not a valid index'):
+            # peak pos exceeds x.size
+            peak_widths(np.arange(10), [8, 11])
+        with raises(ValueError, match='not a valid index'):
+            # empty x with peaks supplied
+            peak_widths([], [1, 2])
+        with raises(TypeError, match='cannot safely cast'):
+            # peak cannot be safely casted to intp
+            peak_widths(np.arange(10), [1.1, 2.3])
+        with raises(ValueError, match='rel_height'):
+            # rel_height is < 0
+            peak_widths([0, 1, 0, 1, 0], [1, 3], rel_height=-1)
+        with raises(TypeError, match='None'):
+            # prominence data contains None
+            peak_widths([1, 2, 1], [1], prominence_data=(None, None, None))
+
+    def test_warnings(self):
+        """
+        Verify that appropriate warnings are raised.
+        """
+        msg = "some peaks have a width of 0"
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: rel_height is 0
+            peak_widths([0, 1, 0], [1], rel_height=0)
+        with warns(PeakPropertyWarning, match=msg):
+            # Case: prominence is 0 and bases are identical
+            peak_widths(
+                [0, 1, 1, 1, 0], [2],
+                prominence_data=(np.array([0.], np.float64),
+                                 np.array([2], np.intp),
+                                 np.array([2], np.intp))
+            )
+
+    def test_mismatching_prominence_data(self):
+        """Test with mismatching peak and / or prominence data."""
+        x = [0, 1, 0]
+        peak = [1]
+        for i, (prominences, left_bases, right_bases) in enumerate([
+            ((1.,), (-1,), (2,)),  # left base not in x
+            ((1.,), (0,), (3,)),  # right base not in x
+            ((1.,), (2,), (0,)),  # swapped bases same as peak
+            ((1., 1.), (0, 0), (2, 2)),  # array shapes don't match peaks
+            ((1., 1.), (0,), (2,)),  # arrays with different shapes
+            ((1.,), (0, 0), (2,)),  # arrays with different shapes
+            ((1.,), (0,), (2, 2))  # arrays with different shapes
+        ]):
+            # Make sure input is matches output of signal.peak_prominences
+            prominence_data = (np.array(prominences, dtype=np.float64),
+                               np.array(left_bases, dtype=np.intp),
+                               np.array(right_bases, dtype=np.intp))
+            # Test for correct exception
+            if i < 3:
+                match = "prominence data is invalid for peak"
+            else:
+                match = "arrays in `prominence_data` must have the same shape"
+            with raises(ValueError, match=match):
+                peak_widths(x, peak, prominence_data=prominence_data)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a width of 0")
+    def test_intersection_rules(self):
+        """Test if x == eval_height counts as an intersection."""
+        # Flatt peak with two possible intersection points if evaluated at 1
+        x = [0, 1, 2, 1, 3, 3, 3, 1, 2, 1, 0]
+        # relative height is 0 -> width is 0 as well, raises warning
+        assert_allclose(peak_widths(x, peaks=[5], rel_height=0),
+                        [(0.,), (3.,), (5.,), (5.,)])
+        # width_height == x counts as intersection -> nearest 1 is chosen
+        assert_allclose(peak_widths(x, peaks=[5], rel_height=2/3),
+                        [(4.,), (1.,), (3.,), (7.,)])
+
+
+def test_unpack_condition_args():
+    """
+    Verify parsing of condition arguments for `scipy.signal.find_peaks` function.
+    """
+    x = np.arange(10)
+    amin_true = x
+    amax_true = amin_true + 10
+    peaks = amin_true[1::2]
+
+    # Test unpacking with None or interval
+    assert_((None, None) == _unpack_condition_args((None, None), x, peaks))
+    assert_((1, None) == _unpack_condition_args(1, x, peaks))
+    assert_((1, None) == _unpack_condition_args((1, None), x, peaks))
+    assert_((None, 2) == _unpack_condition_args((None, 2), x, peaks))
+    assert_((3., 4.5) == _unpack_condition_args((3., 4.5), x, peaks))
+
+    # Test if borders are correctly reduced with `peaks`
+    amin_calc, amax_calc = _unpack_condition_args((amin_true, amax_true), x, peaks)
+    assert_equal(amin_calc, amin_true[peaks])
+    assert_equal(amax_calc, amax_true[peaks])
+
+    # Test raises if array borders don't match x
+    with raises(ValueError, match="array size of lower"):
+        _unpack_condition_args(amin_true, np.arange(11), peaks)
+    with raises(ValueError, match="array size of upper"):
+        _unpack_condition_args((None, amin_true), np.arange(11), peaks)
+
+
+class TestFindPeaks(object):
+
+    # Keys of optionally returned properties
+    property_keys = {'peak_heights', 'left_thresholds', 'right_thresholds',
+                     'prominences', 'left_bases', 'right_bases', 'widths',
+                     'width_heights', 'left_ips', 'right_ips'}
+
+    def test_constant(self):
+        """
+        Test behavior for signal without local maxima.
+        """
+        open_interval = (None, None)
+        peaks, props = find_peaks(np.ones(10),
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert_(peaks.size == 0)
+        for key in self.property_keys:
+            assert_(props[key].size == 0)
+
+    def test_plateau_size(self):
+        """
+        Test plateau size condition for peaks.
+        """
+        # Prepare signal with peaks with peak_height == plateau_size
+        plateau_sizes = np.array([1, 2, 3, 4, 8, 20, 111])
+        x = np.zeros(plateau_sizes.size * 2 + 1)
+        x[1::2] = plateau_sizes
+        repeats = np.ones(x.size, dtype=int)
+        repeats[1::2] = x[1::2]
+        x = np.repeat(x, repeats)
+
+        # Test full output
+        peaks, props = find_peaks(x, plateau_size=(None, None))
+        assert_equal(peaks, [1, 3, 7, 11, 18, 33, 100])
+        assert_equal(props["plateau_sizes"], plateau_sizes)
+        assert_equal(props["left_edges"], peaks - (plateau_sizes - 1) // 2)
+        assert_equal(props["right_edges"], peaks + plateau_sizes // 2)
+
+        # Test conditions
+        assert_equal(find_peaks(x, plateau_size=4)[0], [11, 18, 33, 100])
+        assert_equal(find_peaks(x, plateau_size=(None, 3.5))[0], [1, 3, 7])
+        assert_equal(find_peaks(x, plateau_size=(5, 50))[0], [18, 33])
+
+    def test_height_condition(self):
+        """
+        Test height condition for peaks.
+        """
+        x = (0., 1/3, 0., 2.5, 0, 4., 0)
+        peaks, props = find_peaks(x, height=(None, None))
+        assert_equal(peaks, np.array([1, 3, 5]))
+        assert_equal(props['peak_heights'], np.array([1/3, 2.5, 4.]))
+        assert_equal(find_peaks(x, height=0.5)[0], np.array([3, 5]))
+        assert_equal(find_peaks(x, height=(None, 3))[0], np.array([1, 3]))
+        assert_equal(find_peaks(x, height=(2, 3))[0], np.array([3]))
+
+    def test_threshold_condition(self):
+        """
+        Test threshold condition for peaks.
+        """
+        x = (0, 2, 1, 4, -1)
+        peaks, props = find_peaks(x, threshold=(None, None))
+        assert_equal(peaks, np.array([1, 3]))
+        assert_equal(props['left_thresholds'], np.array([2, 3]))
+        assert_equal(props['right_thresholds'], np.array([1, 5]))
+        assert_equal(find_peaks(x, threshold=2)[0], np.array([3]))
+        assert_equal(find_peaks(x, threshold=3.5)[0], np.array([]))
+        assert_equal(find_peaks(x, threshold=(None, 5))[0], np.array([1, 3]))
+        assert_equal(find_peaks(x, threshold=(None, 4))[0], np.array([1]))
+        assert_equal(find_peaks(x, threshold=(2, 4))[0], np.array([]))
+
+    def test_distance_condition(self):
+        """
+        Test distance condition for peaks.
+        """
+        # Peaks of different height with constant distance 3
+        peaks_all = np.arange(1, 21, 3)
+        x = np.zeros(21)
+        x[peaks_all] += np.linspace(1, 2, peaks_all.size)
+
+        # Test if peaks with "minimal" distance are still selected (distance = 3)
+        assert_equal(find_peaks(x, distance=3)[0], peaks_all)
+
+        # Select every second peak (distance > 3)
+        peaks_subset = find_peaks(x, distance=3.0001)[0]
+        # Test if peaks_subset is subset of peaks_all
+        assert_(
+            np.setdiff1d(peaks_subset, peaks_all, assume_unique=True).size == 0
+        )
+        # Test if every second peak was removed
+        assert_equal(np.diff(peaks_subset), 6)
+
+        # Test priority of peak removal
+        x = [-2, 1, -1, 0, -3]
+        peaks_subset = find_peaks(x, distance=10)[0]  # use distance > x size
+        assert_(peaks_subset.size == 1 and peaks_subset[0] == 1)
+
+    def test_prominence_condition(self):
+        """
+        Test prominence condition for peaks.
+        """
+        x = np.linspace(0, 10, 100)
+        peaks_true = np.arange(1, 99, 2)
+        offset = np.linspace(1, 10, peaks_true.size)
+        x[peaks_true] += offset
+        prominences = x[peaks_true] - x[peaks_true + 1]
+        interval = (3, 9)
+        keep = np.nonzero(
+            (interval[0] <= prominences) & (prominences <= interval[1]))
+
+        peaks_calc, properties = find_peaks(x, prominence=interval)
+        assert_equal(peaks_calc, peaks_true[keep])
+        assert_equal(properties['prominences'], prominences[keep])
+        assert_equal(properties['left_bases'], 0)
+        assert_equal(properties['right_bases'], peaks_true[keep] + 1)
+
+    def test_width_condition(self):
+        """
+        Test width condition for peaks.
+        """
+        x = np.array([1, 0, 1, 2, 1, 0, -1, 4, 0])
+        peaks, props = find_peaks(x, width=(None, 2), rel_height=0.75)
+        assert_equal(peaks.size, 1)
+        assert_equal(peaks, 7)
+        assert_allclose(props['widths'], 1.35)
+        assert_allclose(props['width_heights'], 1.)
+        assert_allclose(props['left_ips'], 6.4)
+        assert_allclose(props['right_ips'], 7.75)
+
+    def test_properties(self):
+        """
+        Test returned properties.
+        """
+        open_interval = (None, None)
+        x = [0, 1, 0, 2, 1.5, 0, 3, 0, 5, 9]
+        peaks, props = find_peaks(x,
+                                  height=open_interval, threshold=open_interval,
+                                  prominence=open_interval, width=open_interval)
+        assert_(len(props) == len(self.property_keys))
+        for key in self.property_keys:
+            assert_(peaks.size == props[key].size)
+
+    def test_raises(self):
+        """
+        Test exceptions raised by function.
+        """
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.array(1))
+        with raises(ValueError, match="1-D array"):
+            find_peaks(np.ones((2, 2)))
+        with raises(ValueError, match="distance"):
+            find_peaks(np.arange(10), distance=-1)
+
+    @pytest.mark.filterwarnings("ignore:some peaks have a prominence of 0",
+                                "ignore:some peaks have a width of 0")
+    def test_wlen_smaller_plateau(self):
+        """
+        Test behavior of prominence and width calculation if the given window
+        length is smaller than a peak's plateau size.
+
+        Regression test for gh-9110.
+        """
+        peaks, props = find_peaks([0, 1, 1, 1, 0], prominence=(None, None),
+                                  width=(None, None), wlen=2)
+        assert_equal(peaks, 2)
+        assert_equal(props["prominences"], 0)
+        assert_equal(props["widths"], 0)
+        assert_equal(props["width_heights"], 1)
+        for key in ("left_bases", "right_bases", "left_ips", "right_ips"):
+            assert_equal(props[key], peaks)
+
+
+class TestFindPeaksCwt(object):
+
+    def test_find_peaks_exact(self):
+        """
+        Generate a series of gaussians and attempt to find the peak locations.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=0,
+                                         min_length=None)
+        np.testing.assert_array_equal(found_locs, act_locs,
+                        "Found maximum locations did not equal those expected")
+
+    def test_find_peaks_withnoise(self):
+        """
+        Verify that peak locations are (approximately) found
+        for a series of gaussians with added noise.
+        """
+        sigmas = [5.0, 3.0, 10.0, 20.0, 10.0, 50.0]
+        num_points = 500
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas))
+        noise_amp = 0.07
+        np.random.seed(18181911)
+        test_data += (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+        found_locs = find_peaks_cwt(test_data, widths, min_length=15,
+                                         gap_thresh=1, min_snr=noise_amp / 5)
+
+        np.testing.assert_equal(len(found_locs), len(act_locs), 'Different number' +
+                                'of peaks found than expected')
+        diffs = np.abs(found_locs - act_locs)
+        max_diffs = np.array(sigmas) / 5
+        np.testing.assert_array_less(diffs, max_diffs, 'Maximum location differed' +
+                                     'by more than %s' % (max_diffs))
+
+    def test_find_peaks_nopeak(self):
+        """
+        Verify that no peak is found in
+        data that's just noise.
+        """
+        noise_amp = 1.0
+        num_points = 100
+        np.random.seed(181819141)
+        test_data = (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+        widths = np.arange(10, 50)
+        found_locs = find_peaks_cwt(test_data, widths, min_snr=5, noise_perc=30)
+        np.testing.assert_equal(len(found_locs), 0)
+
+    def test_find_peaks_window_size(self):
+        """
+        Verify that window_size is passed correctly to private function and
+        affects the result.
+        """
+        sigmas = [2.0, 2.0]
+        num_points = 1000
+        test_data, act_locs = _gen_gaussians_even(sigmas, num_points)
+        widths = np.arange(0.1, max(sigmas), 0.2)
+        noise_amp = 0.05
+        np.random.seed(18181911)
+        test_data += (np.random.rand(num_points) - 0.5)*(2*noise_amp)
+
+        # Possibly contrived negative region to throw off peak finding
+        # when window_size is too large
+        test_data[250:320] -= 1
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=None)
+        with pytest.raises(AssertionError):
+            assert found_locs.size == act_locs.size
+
+        found_locs = find_peaks_cwt(test_data, widths, gap_thresh=2, min_snr=3,
+                                    min_length=None, window_size=20)
+        assert found_locs.size == act_locs.size

venv/Lib/site-packages/scipy/signal/tests/test_savitzky_golay.py

@@ -0,0 +1,301 @@
+import numpy as np
+from numpy.testing import (assert_allclose, assert_equal,
+                           assert_almost_equal, assert_array_equal,
+                           assert_array_almost_equal)
+
+from scipy.ndimage import convolve1d
+
+from scipy.signal import savgol_coeffs, savgol_filter
+from scipy.signal._savitzky_golay import _polyder
+
+
+def check_polyder(p, m, expected):
+    dp = _polyder(p, m)
+    assert_array_equal(dp, expected)
+
+
+def test_polyder():
+    cases = [
+        ([5], 0, [5]),
+        ([5], 1, [0]),
+        ([3, 2, 1], 0, [3, 2, 1]),
+        ([3, 2, 1], 1, [6, 2]),
+        ([3, 2, 1], 2, [6]),
+        ([3, 2, 1], 3, [0]),
+        ([[3, 2, 1], [5, 6, 7]], 0, [[3, 2, 1], [5, 6, 7]]),
+        ([[3, 2, 1], [5, 6, 7]], 1, [[6, 2], [10, 6]]),
+        ([[3, 2, 1], [5, 6, 7]], 2, [[6], [10]]),
+        ([[3, 2, 1], [5, 6, 7]], 3, [[0], [0]]),
+    ]
+    for p, m, expected in cases:
+        check_polyder(np.array(p).T, m, np.array(expected).T)
+
+
+#--------------------------------------------------------------------
+# savgol_coeffs tests
+#--------------------------------------------------------------------
+
+def alt_sg_coeffs(window_length, polyorder, pos):
+    """This is an alternative implementation of the SG coefficients.
+
+    It uses numpy.polyfit and numpy.polyval. The results should be
+    equivalent to those of savgol_coeffs(), but this implementation
+    is slower.
+
+    window_length should be odd.
+
+    """
+    if pos is None:
+        pos = window_length // 2
+    t = np.arange(window_length)
+    unit = (t == pos).astype(int)
+    h = np.polyval(np.polyfit(t, unit, polyorder), t)
+    return h
+
+
+def test_sg_coeffs_trivial():
+    # Test a trivial case of savgol_coeffs: polyorder = window_length - 1
+    h = savgol_coeffs(1, 0)
+    assert_allclose(h, [1])
+
+    h = savgol_coeffs(3, 2)
+    assert_allclose(h, [0, 1, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4)
+    assert_allclose(h, [0, 0, 1, 0, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1)
+    assert_allclose(h, [0, 0, 0, 1, 0], atol=1e-10)
+
+    h = savgol_coeffs(5, 4, pos=1, use='dot')
+    assert_allclose(h, [0, 1, 0, 0, 0], atol=1e-10)
+
+
+def compare_coeffs_to_alt(window_length, order):
+    # For the given window_length and order, compare the results
+    # of savgol_coeffs and alt_sg_coeffs for pos from 0 to window_length - 1.
+    # Also include pos=None.
+    for pos in [None] + list(range(window_length)):
+        h1 = savgol_coeffs(window_length, order, pos=pos, use='dot')
+        h2 = alt_sg_coeffs(window_length, order, pos=pos)
+        assert_allclose(h1, h2, atol=1e-10,
+                        err_msg=("window_length = %d, order = %d, pos = %s" %
+                                 (window_length, order, pos)))
+
+
+def test_sg_coeffs_compare():
+    # Compare savgol_coeffs() to alt_sg_coeffs().
+    for window_length in range(1, 8, 2):
+        for order in range(window_length):
+            compare_coeffs_to_alt(window_length, order)
+
+
+def test_sg_coeffs_exact():
+    polyorder = 4
+    window_length = 9
+    halflen = window_length // 2
+
+    x = np.linspace(0, 21, 43)
+    delta = x[1] - x[0]
+
+    # The data is a cubic polynomial.  We'll use an order 4
+    # SG filter, so the filtered values should equal the input data
+    # (except within half window_length of the edges).
+    y = 0.5 * x ** 3 - x
+    h = savgol_coeffs(window_length, polyorder)
+    y0 = convolve1d(y, h)
+    assert_allclose(y0[halflen:-halflen], y[halflen:-halflen])
+
+    # Check the same input, but use deriv=1.  dy is the exact result.
+    dy = 1.5 * x ** 2 - 1
+    h = savgol_coeffs(window_length, polyorder, deriv=1, delta=delta)
+    y1 = convolve1d(y, h)
+    assert_allclose(y1[halflen:-halflen], dy[halflen:-halflen])
+
+    # Check the same input, but use deriv=2. d2y is the exact result.
+    d2y = 3.0 * x
+    h = savgol_coeffs(window_length, polyorder, deriv=2, delta=delta)
+    y2 = convolve1d(y, h)
+    assert_allclose(y2[halflen:-halflen], d2y[halflen:-halflen])
+
+
+def test_sg_coeffs_deriv():
+    # The data in `x` is a sampled parabola, so using savgol_coeffs with an
+    # order 2 or higher polynomial should give exact results.
+    i = np.array([-2.0, 0.0, 2.0, 4.0, 6.0])
+    x = i ** 2 / 4
+    dx = i / 2
+    d2x = np.full_like(i, 0.5)
+    for pos in range(x.size):
+        coeffs0 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot')
+        assert_allclose(coeffs0.dot(x), x[pos], atol=1e-10)
+        coeffs1 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=1)
+        assert_allclose(coeffs1.dot(x), dx[pos], atol=1e-10)
+        coeffs2 = savgol_coeffs(5, 3, pos=pos, delta=2.0, use='dot', deriv=2)
+        assert_allclose(coeffs2.dot(x), d2x[pos], atol=1e-10)
+
+
+def test_sg_coeffs_deriv_gt_polyorder():
+    """
+    If deriv > polyorder, the coefficients should be all 0.
+    This is a regression test for a bug where, e.g.,
+        savgol_coeffs(5, polyorder=1, deriv=2)
+    raised an error.
+    """
+    coeffs = savgol_coeffs(5, polyorder=1, deriv=2)
+    assert_array_equal(coeffs, np.zeros(5))
+    coeffs = savgol_coeffs(7, polyorder=4, deriv=6)
+    assert_array_equal(coeffs, np.zeros(7))
+
+
+def test_sg_coeffs_large():
+    # Test that for large values of window_length and polyorder the array of
+    # coefficients returned is symmetric. The aim is to ensure that
+    # no potential numeric overflow occurs.
+    coeffs0 = savgol_coeffs(31, 9)
+    assert_array_almost_equal(coeffs0, coeffs0[::-1])
+    coeffs1 = savgol_coeffs(31, 9, deriv=1)
+    assert_array_almost_equal(coeffs1, -coeffs1[::-1])
+
+
+#--------------------------------------------------------------------
+# savgol_filter tests
+#--------------------------------------------------------------------
+
+
+def test_sg_filter_trivial():
+    """ Test some trivial edge cases for savgol_filter()."""
+    x = np.array([1.0])
+    y = savgol_filter(x, 1, 0)
+    assert_equal(y, [1.0])
+
+    # Input is a single value. With a window length of 3 and polyorder 1,
+    # the value in y is from the straight-line fit of (-1,0), (0,3) and
+    # (1, 0) at 0. This is just the average of the three values, hence 1.0.
+    x = np.array([3.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_almost_equal(y, [1.0], decimal=15)
+
+    x = np.array([3.0])
+    y = savgol_filter(x, 3, 1, mode='nearest')
+    assert_almost_equal(y, [3.0], decimal=15)
+
+    x = np.array([1.0] * 3)
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    assert_almost_equal(y, [1.0, 1.0, 1.0], decimal=15)
+
+
+def test_sg_filter_basic():
+    # Some basic test cases for savgol_filter().
+    x = np.array([1.0, 2.0, 1.0])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_allclose(y, [1.0, 4.0 / 3, 1.0])
+
+    y = savgol_filter(x, 3, 1, mode='mirror')
+    assert_allclose(y, [5.0 / 3, 4.0 / 3, 5.0 / 3])
+
+    y = savgol_filter(x, 3, 1, mode='wrap')
+    assert_allclose(y, [4.0 / 3, 4.0 / 3, 4.0 / 3])
+
+
+def test_sg_filter_2d():
+    x = np.array([[1.0, 2.0, 1.0],
+                  [2.0, 4.0, 2.0]])
+    expected = np.array([[1.0, 4.0 / 3, 1.0],
+                         [2.0, 8.0 / 3, 2.0]])
+    y = savgol_filter(x, 3, 1, mode='constant')
+    assert_allclose(y, expected)
+
+    y = savgol_filter(x.T, 3, 1, mode='constant', axis=0)
+    assert_allclose(y, expected.T)
+
+
+def test_sg_filter_interp_edges():
+    # Another test with low degree polynomial data, for which we can easily
+    # give the exact results. In this test, we use mode='interp', so
+    # savgol_filter should match the exact solution for the entire data set,
+    # including the edges.
+    t = np.linspace(-5, 5, 21)
+    delta = t[1] - t[0]
+    # Polynomial test data.
+    x = np.array([t,
+                  3 * t ** 2,
+                  t ** 3 - t])
+    dx = np.array([np.ones_like(t),
+                   6 * t,
+                   3 * t ** 2 - 1.0])
+    d2x = np.array([np.zeros_like(t),
+                    np.full_like(t, 6),
+                    6 * t])
+
+    window_length = 7
+
+    y = savgol_filter(x, window_length, 3, axis=-1, mode='interp')
+    assert_allclose(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=1, delta=delta)
+    assert_allclose(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=-1, mode='interp',
+                       deriv=2, delta=delta)
+    assert_allclose(y2, d2x, atol=1e-12)
+
+    # Transpose everything, and test again with axis=0.
+
+    x = x.T
+    dx = dx.T
+    d2x = d2x.T
+
+    y = savgol_filter(x, window_length, 3, axis=0, mode='interp')
+    assert_allclose(y, x, atol=1e-12)
+
+    y1 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=1, delta=delta)
+    assert_allclose(y1, dx, atol=1e-12)
+
+    y2 = savgol_filter(x, window_length, 3, axis=0, mode='interp',
+                       deriv=2, delta=delta)
+    assert_allclose(y2, d2x, atol=1e-12)
+
+
+def test_sg_filter_interp_edges_3d():
+    # Test mode='interp' with a 3-D array.
+    t = np.linspace(-5, 5, 21)
+    delta = t[1] - t[0]
+    x1 = np.array([t, -t])
+    x2 = np.array([t ** 2, 3 * t ** 2 + 5])
+    x3 = np.array([t ** 3, 2 * t ** 3 + t ** 2 - 0.5 * t])
+    dx1 = np.array([np.ones_like(t), -np.ones_like(t)])
+    dx2 = np.array([2 * t, 6 * t])
+    dx3 = np.array([3 * t ** 2, 6 * t ** 2 + 2 * t - 0.5])
+
+    # z has shape (3, 2, 21)
+    z = np.array([x1, x2, x3])
+    dz = np.array([dx1, dx2, dx3])
+
+    y = savgol_filter(z, 7, 3, axis=-1, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=-1, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)
+
+    # z has shape (3, 21, 2)
+    z = np.array([x1.T, x2.T, x3.T])
+    dz = np.array([dx1.T, dx2.T, dx3.T])
+
+    y = savgol_filter(z, 7, 3, axis=1, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=1, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)
+
+    # z has shape (21, 3, 2)
+    z = z.swapaxes(0, 1).copy()
+    dz = dz.swapaxes(0, 1).copy()
+
+    y = savgol_filter(z, 7, 3, axis=0, mode='interp', delta=delta)
+    assert_allclose(y, z, atol=1e-10)
+
+    dy = savgol_filter(z, 7, 3, axis=0, mode='interp', deriv=1, delta=delta)
+    assert_allclose(dy, dz, atol=1e-10)

venv/Lib/site-packages/scipy/signal/tests/test_upfirdn.py

@@ -0,0 +1,273 @@
+# Code adapted from "upfirdn" python library with permission:
+#
+# Copyright (c) 2009, Motorola, Inc
+#
+# All Rights Reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions are
+# met:
+#
+# * Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# * Redistributions in binary form must reproduce the above copyright
+# notice, this list of conditions and the following disclaimer in the
+# documentation and/or other materials provided with the distribution.
+#
+# * Neither the name of Motorola nor the names of its contributors may be
+# used to endorse or promote products derived from this software without
+# specific prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+import numpy as np
+from itertools import product
+
+from numpy.testing import assert_equal, assert_allclose
+from pytest import raises as assert_raises
+import pytest
+
+from scipy.signal import upfirdn, firwin
+from scipy.signal._upfirdn import _output_len, _upfirdn_modes
+from scipy.signal._upfirdn_apply import _pad_test
+
+
+def upfirdn_naive(x, h, up=1, down=1):
+    """Naive upfirdn processing in Python.
+
+    Note: arg order (x, h) differs to facilitate apply_along_axis use.
+    """
+    h = np.asarray(h)
+    out = np.zeros(len(x) * up, x.dtype)
+    out[::up] = x
+    out = np.convolve(h, out)[::down][:_output_len(len(h), len(x), up, down)]
+    return out
+
+
+class UpFIRDnCase(object):
+    """Test _UpFIRDn object"""
+    def __init__(self, up, down, h, x_dtype):
+        self.up = up
+        self.down = down
+        self.h = np.atleast_1d(h)
+        self.x_dtype = x_dtype
+        self.rng = np.random.RandomState(17)
+
+    def __call__(self):
+        # tiny signal
+        self.scrub(np.ones(1, self.x_dtype))
+        # ones
+        self.scrub(np.ones(10, self.x_dtype))  # ones
+        # randn
+        x = self.rng.randn(10).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(10)
+        self.scrub(x)
+        # ramp
+        self.scrub(np.arange(10).astype(self.x_dtype))
+        # 3D, random
+        size = (2, 3, 5)
+        x = self.rng.randn(*size).astype(self.x_dtype)
+        if self.x_dtype in (np.complex64, np.complex128):
+            x += 1j * self.rng.randn(*size)
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+        x = x[:, ::2, 1::3].T
+        for axis in range(len(size)):
+            self.scrub(x, axis=axis)
+
+    def scrub(self, x, axis=-1):
+        yr = np.apply_along_axis(upfirdn_naive, axis, x,
+                                 self.h, self.up, self.down)
+        want_len = _output_len(len(self.h), x.shape[axis], self.up, self.down)
+        assert yr.shape[axis] == want_len
+        y = upfirdn(self.h, x, self.up, self.down, axis=axis)
+        assert y.shape[axis] == want_len
+        assert y.shape == yr.shape
+        dtypes = (self.h.dtype, x.dtype)
+        if all(d == np.complex64 for d in dtypes):
+            assert_equal(y.dtype, np.complex64)
+        elif np.complex64 in dtypes and np.float32 in dtypes:
+            assert_equal(y.dtype, np.complex64)
+        elif all(d == np.float32 for d in dtypes):
+            assert_equal(y.dtype, np.float32)
+        elif np.complex128 in dtypes or np.complex64 in dtypes:
+            assert_equal(y.dtype, np.complex128)
+        else:
+            assert_equal(y.dtype, np.float64)
+        assert_allclose(yr, y)
+
+
+_UPFIRDN_TYPES = (int, np.float32, np.complex64, float, complex)
+
+
+class TestUpfirdn(object):
+
+    def test_valid_input(self):
+        assert_raises(ValueError, upfirdn, [1], [1], 1, 0)  # up or down < 1
+        assert_raises(ValueError, upfirdn, [], [1], 1, 1)  # h.ndim != 1
+        assert_raises(ValueError, upfirdn, [[1]], [1], 1, 1)
+
+    @pytest.mark.parametrize('len_h', [1, 2, 3, 4, 5])
+    @pytest.mark.parametrize('len_x', [1, 2, 3, 4, 5])
+    def test_singleton(self, len_h, len_x):
+        # gh-9844: lengths producing expected outputs
+        h = np.zeros(len_h)
+        h[len_h // 2] = 1.  # make h a delta
+        x = np.ones(len_x)
+        y = upfirdn(h, x, 1, 1)
+        want = np.pad(x, (len_h // 2, (len_h - 1) // 2), 'constant')
+        assert_allclose(y, want)
+
+    def test_shift_x(self):
+        # gh-9844: shifted x can change values?
+        y = upfirdn([1, 1], [1.], 1, 1)
+        assert_allclose(y, [1, 1])  # was [0, 1] in the issue
+        y = upfirdn([1, 1], [0., 1.], 1, 1)
+        assert_allclose(y, [0, 1, 1])
+
+    # A bunch of lengths/factors chosen because they exposed differences
+    # between the "old way" and new way of computing length, and then
+    # got `expected` from MATLAB
+    @pytest.mark.parametrize('len_h, len_x, up, down, expected', [
+        (2, 2, 5, 2, [1, 0, 0, 0]),
+        (2, 3, 6, 3, [1, 0, 1, 0, 1]),
+        (2, 4, 4, 3, [1, 0, 0, 0, 1]),
+        (3, 2, 6, 2, [1, 0, 0, 1, 0]),
+        (4, 11, 3, 5, [1, 0, 0, 1, 0, 0, 1]),
+    ])
+    def test_length_factors(self, len_h, len_x, up, down, expected):
+        # gh-9844: weird factors
+        h = np.zeros(len_h)
+        h[0] = 1.
+        x = np.ones(len_x)
+        y = upfirdn(h, x, up, down)
+        assert_allclose(y, expected)
+
+    @pytest.mark.parametrize('down, want_len', [  # lengths from MATLAB
+        (2, 5015),
+        (11, 912),
+        (79, 127),
+    ])
+    def test_vs_convolve(self, down, want_len):
+        # Check that up=1.0 gives same answer as convolve + slicing
+        random_state = np.random.RandomState(17)
+        try_types = (int, np.float32, np.complex64, float, complex)
+        size = 10000
+
+        for dtype in try_types:
+            x = random_state.randn(size).astype(dtype)
+            if dtype in (np.complex64, np.complex128):
+                x += 1j * random_state.randn(size)
+
+            h = firwin(31, 1. / down, window='hamming')
+            yl = upfirdn_naive(x, h, 1, down)
+            y = upfirdn(h, x, up=1, down=down)
+            assert y.shape == (want_len,)
+            assert yl.shape[0] == y.shape[0]
+            assert_allclose(yl, y, atol=1e-7, rtol=1e-7)
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h', (1., 1j))
+    @pytest.mark.parametrize('up, down', [(1, 1), (2, 2), (3, 2), (2, 3)])
+    def test_vs_naive_delta(self, x_dtype, h, up, down):
+        UpFIRDnCase(up, down, h, x_dtype)()
+
+    @pytest.mark.parametrize('x_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('h_dtype', _UPFIRDN_TYPES)
+    @pytest.mark.parametrize('p_max, q_max',
+                             list(product((10, 100), (10, 100))))
+    def test_vs_naive(self, x_dtype, h_dtype, p_max, q_max):
+        tests = self._random_factors(p_max, q_max, h_dtype, x_dtype)
+        for test in tests:
+            test()
+
+    def _random_factors(self, p_max, q_max, h_dtype, x_dtype):
+        n_rep = 3
+        longest_h = 25
+        random_state = np.random.RandomState(17)
+        tests = []
+
+        for _ in range(n_rep):
+            # Randomize the up/down factors somewhat
+            p_add = q_max if p_max > q_max else 1
+            q_add = p_max if q_max > p_max else 1
+            p = random_state.randint(p_max) + p_add
+            q = random_state.randint(q_max) + q_add
+
+            # Generate random FIR coefficients
+            len_h = random_state.randint(longest_h) + 1
+            h = np.atleast_1d(random_state.randint(len_h))
+            h = h.astype(h_dtype)
+            if h_dtype == complex:
+                h += 1j * random_state.randint(len_h)
+
+            tests.append(UpFIRDnCase(p, q, h, x_dtype))
+
+        return tests
+
+    @pytest.mark.parametrize('mode', _upfirdn_modes)
+    def test_extensions(self, mode):
+        """Test vs. manually computed results for modes not in numpy's pad."""
+        x = np.array([1, 2, 3, 1], dtype=float)
+        npre, npost = 6, 6
+        y = _pad_test(x, npre=npre, npost=npost, mode=mode)
+        if mode == 'antisymmetric':
+            y_expected = np.asarray(
+                [3, 1, -1, -3, -2, -1, 1, 2, 3, 1, -1, -3, -2, -1, 1, 2])
+        elif mode == 'antireflect':
+            y_expected = np.asarray(
+                [1, 2, 3, 1, -1, 0, 1, 2, 3, 1, -1, 0, 1, 2, 3, 1])
+        elif mode == 'smooth':
+            y_expected = np.asarray(
+                [-5, -4, -3, -2, -1, 0, 1, 2, 3, 1, -1, -3, -5, -7, -9, -11])
+        elif mode == "line":
+            lin_slope = (x[-1] - x[0]) / (len(x) - 1)
+            left = x[0] + np.arange(-npre, 0, 1) * lin_slope
+            right = x[-1] + np.arange(1, npost + 1) * lin_slope
+            y_expected = np.concatenate((left, x, right))
+        else:
+            y_expected = np.pad(x, (npre, npost), mode=mode)
+        assert_allclose(y, y_expected)
+
+    @pytest.mark.parametrize(
+        'size, h_len, mode, dtype',
+        product(
+            [8],
+            [4, 5, 26],  # include cases with h_len > 2*size
+            _upfirdn_modes,
+            [np.float32, np.float64, np.complex64, np.complex128],
+        )
+    )
+    def test_modes(self, size, h_len, mode, dtype):
+        random_state = np.random.RandomState(5)
+        x = random_state.randn(size).astype(dtype)
+        if dtype in (np.complex64, np.complex128):
+            x += 1j * random_state.randn(size)
+        h = np.arange(1, 1 + h_len, dtype=x.real.dtype)
+
+        y = upfirdn(h, x, up=1, down=1, mode=mode)
+        # expected result: pad the input, filter with zero padding, then crop
+        npad = h_len - 1
+        if mode in ['antisymmetric', 'antireflect', 'smooth', 'line']:
+            # use _pad_test test function for modes not supported by np.pad.
+            xpad = _pad_test(x, npre=npad, npost=npad, mode=mode)
+        else:
+            xpad = np.pad(x, npad, mode=mode)
+        ypad = upfirdn(h, xpad, up=1, down=1, mode='constant')
+        y_expected = ypad[npad:-npad]
+
+        atol = rtol = np.finfo(dtype).eps * 1e2
+        assert_allclose(y, y_expected, atol=atol, rtol=rtol)

venv/Lib/site-packages/scipy/signal/tests/test_waveforms.py

@@ -0,0 +1,351 @@
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_equal,
+                           assert_, assert_allclose, assert_array_equal)
+from pytest import raises as assert_raises
+
+import scipy.signal.waveforms as waveforms
+
+
+# These chirp_* functions are the instantaneous frequencies of the signals
+# returned by chirp().
+
+def chirp_linear(t, f0, f1, t1):
+    f = f0 + (f1 - f0) * t / t1
+    return f
+
+
+def chirp_quadratic(t, f0, f1, t1, vertex_zero=True):
+    if vertex_zero:
+        f = f0 + (f1 - f0) * t**2 / t1**2
+    else:
+        f = f1 - (f1 - f0) * (t1 - t)**2 / t1**2
+    return f
+
+
+def chirp_geometric(t, f0, f1, t1):
+    f = f0 * (f1/f0)**(t/t1)
+    return f
+
+
+def chirp_hyperbolic(t, f0, f1, t1):
+    f = f0*f1*t1 / ((f0 - f1)*t + f1*t1)
+    return f
+
+
+def compute_frequency(t, theta):
+    """
+    Compute theta'(t)/(2*pi), where theta'(t) is the derivative of theta(t).
+    """
+    # Assume theta and t are 1-D NumPy arrays.
+    # Assume that t is uniformly spaced.
+    dt = t[1] - t[0]
+    f = np.diff(theta)/(2*np.pi) / dt
+    tf = 0.5*(t[1:] + t[:-1])
+    return tf, f
+
+
+class TestChirp(object):
+
+    def test_linear_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='linear')
+        assert_almost_equal(w, 1.0)
+
+    def test_linear_freq_01(self):
+        method = 'linear'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_linear_freq_02(self):
+        method = 'linear'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 100)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_linear(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_quadratic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic')
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_at_zero2(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='quadratic',
+                            vertex_zero=False)
+        assert_almost_equal(w, 1.0)
+
+    def test_quadratic_freq_01(self):
+        method = 'quadratic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_quadratic_freq_02(self):
+        method = 'quadratic'
+        f0 = 20.0
+        f1 = 10.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 2000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_quadratic(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=1.0, f1=2.0, t1=1.0, method='logarithmic')
+        assert_almost_equal(w, 1.0)
+
+    def test_logarithmic_freq_01(self):
+        method = 'logarithmic'
+        f0 = 1.0
+        f1 = 2.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_freq_02(self):
+        method = 'logarithmic'
+        f0 = 200.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_logarithmic_freq_03(self):
+        method = 'logarithmic'
+        f0 = 100.0
+        f1 = 100.0
+        t1 = 10.0
+        t = np.linspace(0, t1, 10000)
+        phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+        tf, f = compute_frequency(t, phase)
+        abserr = np.max(np.abs(f - chirp_geometric(tf, f0, f1, t1)))
+        assert_(abserr < 1e-6)
+
+    def test_hyperbolic_at_zero(self):
+        w = waveforms.chirp(t=0, f0=10.0, f1=1.0, t1=1.0, method='hyperbolic')
+        assert_almost_equal(w, 1.0)
+
+    def test_hyperbolic_freq_01(self):
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 10000)
+        #           f0     f1
+        cases = [[10.0, 1.0],
+                 [1.0, 10.0],
+                 [-10.0, -1.0],
+                 [-1.0, -10.0]]
+        for f0, f1 in cases:
+            phase = waveforms._chirp_phase(t, f0, t1, f1, method)
+            tf, f = compute_frequency(t, phase)
+            expected = chirp_hyperbolic(tf, f0, f1, t1)
+            assert_allclose(f, expected)
+
+    def test_hyperbolic_zero_freq(self):
+        # f0=0 or f1=0 must raise a ValueError.
+        method = 'hyperbolic'
+        t1 = 1.0
+        t = np.linspace(0, t1, 5)
+        assert_raises(ValueError, waveforms.chirp, t, 0, t1, 1, method)
+        assert_raises(ValueError, waveforms.chirp, t, 1, t1, 0, method)
+
+    def test_unknown_method(self):
+        method = "foo"
+        f0 = 10.0
+        f1 = 20.0
+        t1 = 1.0
+        t = np.linspace(0, t1, 10)
+        assert_raises(ValueError, waveforms.chirp, t, f0, t1, f1, method)
+
+    def test_integer_t1(self):
+        f0 = 10.0
+        f1 = 20.0
+        t = np.linspace(-1, 1, 11)
+        t1 = 3.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        t1 = 3
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 't1=3' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f0(self):
+        f1 = 20.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f0 = 10.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f0 = 10
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_f1(self):
+        f0 = 10.0
+        t1 = 3.0
+        t = np.linspace(-1, 1, 11)
+        f1 = 20.0
+        float_result = waveforms.chirp(t, f0, t1, f1)
+        f1 = 20
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f1=20' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_all(self):
+        f0 = 10
+        t1 = 3
+        f1 = 20
+        t = np.linspace(-1, 1, 11)
+        float_result = waveforms.chirp(t, float(f0), float(t1), float(f1))
+        int_result = waveforms.chirp(t, f0, t1, f1)
+        err_msg = "Integer input 'f0=10, t1=3, f1=20' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestSweepPoly(object):
+
+    def test_sweep_poly_quad1(self):
+        p = np.poly1d([1.0, 0.0, 1.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_const(self):
+        p = np.poly1d(2.0)
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_linear(self):
+        p = np.poly1d([-1.0, 10.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_quad2(self):
+        p = np.poly1d([1.0, 0.0, -2.0])
+        t = np.linspace(0, 3.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic(self):
+        p = np.poly1d([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = p(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic2(self):
+        """Use an array of coefficients instead of a poly1d."""
+        p = np.array([2.0, 1.0, 0.0, -2.0])
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+    def test_sweep_poly_cubic3(self):
+        """Use a list of coefficients instead of a poly1d."""
+        p = [2.0, 1.0, 0.0, -2.0]
+        t = np.linspace(0, 2.0, 10000)
+        phase = waveforms._sweep_poly_phase(t, p)
+        tf, f = compute_frequency(t, phase)
+        expected = np.poly1d(p)(tf)
+        abserr = np.max(np.abs(f - expected))
+        assert_(abserr < 1e-6)
+
+
+class TestGaussPulse(object):
+
+    def test_integer_fc(self):
+        float_result = waveforms.gausspulse('cutoff', fc=1000.0)
+        int_result = waveforms.gausspulse('cutoff', fc=1000)
+        err_msg = "Integer input 'fc=1000' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bw(self):
+        float_result = waveforms.gausspulse('cutoff', bw=1.0)
+        int_result = waveforms.gausspulse('cutoff', bw=1)
+        err_msg = "Integer input 'bw=1' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_bwr(self):
+        float_result = waveforms.gausspulse('cutoff', bwr=-6.0)
+        int_result = waveforms.gausspulse('cutoff', bwr=-6)
+        err_msg = "Integer input 'bwr=-6' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+    def test_integer_tpr(self):
+        float_result = waveforms.gausspulse('cutoff', tpr=-60.0)
+        int_result = waveforms.gausspulse('cutoff', tpr=-60)
+        err_msg = "Integer input 'tpr=-60' gives wrong result"
+        assert_equal(int_result, float_result, err_msg=err_msg)
+
+
+class TestUnitImpulse(object):
+
+    def test_no_index(self):
+        assert_array_equal(waveforms.unit_impulse(7), [1, 0, 0, 0, 0, 0, 0])
+        assert_array_equal(waveforms.unit_impulse((3, 3)),
+                           [[1, 0, 0], [0, 0, 0], [0, 0, 0]])
+
+    def test_index(self):
+        assert_array_equal(waveforms.unit_impulse(10, 3),
+                           [0, 0, 0, 1, 0, 0, 0, 0, 0, 0])
+        assert_array_equal(waveforms.unit_impulse((3, 3), (1, 1)),
+                           [[0, 0, 0], [0, 1, 0], [0, 0, 0]])
+
+        # Broadcasting
+        imp = waveforms.unit_impulse((4, 4), 2)
+        assert_array_equal(imp, np.array([[0, 0, 0, 0],
+                                          [0, 0, 0, 0],
+                                          [0, 0, 1, 0],
+                                          [0, 0, 0, 0]]))
+
+    def test_mid(self):
+        assert_array_equal(waveforms.unit_impulse((3, 3), 'mid'),
+                           [[0, 0, 0], [0, 1, 0], [0, 0, 0]])
+        assert_array_equal(waveforms.unit_impulse(9, 'mid'),
+                           [0, 0, 0, 0, 1, 0, 0, 0, 0])
+
+    def test_dtype(self):
+        imp = waveforms.unit_impulse(7)
+        assert_(np.issubdtype(imp.dtype, np.floating))
+
+        imp = waveforms.unit_impulse(5, 3, dtype=int)
+        assert_(np.issubdtype(imp.dtype, np.integer))
+
+        imp = waveforms.unit_impulse((5, 2), (3, 1), dtype=complex)
+        assert_(np.issubdtype(imp.dtype, np.complexfloating))

venv/Lib/site-packages/scipy/signal/tests/test_wavelets.py

@@ -0,0 +1,152 @@
+import numpy as np
+from numpy.testing import assert_equal, \
+    assert_array_equal, assert_array_almost_equal, assert_array_less, assert_
+
+from scipy.signal import wavelets
+
+
+class TestWavelets(object):
+    def test_qmf(self):
+        assert_array_equal(wavelets.qmf([1, 1]), [1, -1])
+
+    def test_daub(self):
+        for i in range(1, 15):
+            assert_equal(len(wavelets.daub(i)), i * 2)
+
+    def test_cascade(self):
+        for J in range(1, 7):
+            for i in range(1, 5):
+                lpcoef = wavelets.daub(i)
+                k = len(lpcoef)
+                x, phi, psi = wavelets.cascade(lpcoef, J)
+                assert_(len(x) == len(phi) == len(psi))
+                assert_equal(len(x), (k - 1) * 2 ** J)
+
+    def test_morlet(self):
+        x = wavelets.morlet(50, 4.1, complete=True)
+        y = wavelets.morlet(50, 4.1, complete=False)
+        # Test if complete and incomplete wavelet have same lengths:
+        assert_equal(len(x), len(y))
+        # Test if complete wavelet is less than incomplete wavelet:
+        assert_array_less(x, y)
+
+        x = wavelets.morlet(10, 50, complete=False)
+        y = wavelets.morlet(10, 50, complete=True)
+        # For large widths complete and incomplete wavelets should be
+        # identical within numerical precision:
+        assert_equal(x, y)
+
+        # miscellaneous tests:
+        x = np.array([1.73752399e-09 + 9.84327394e-25j,
+                      6.49471756e-01 + 0.00000000e+00j,
+                      1.73752399e-09 - 9.84327394e-25j])
+        y = wavelets.morlet(3, w=2, complete=True)
+        assert_array_almost_equal(x, y)
+
+        x = np.array([2.00947715e-09 + 9.84327394e-25j,
+                      7.51125544e-01 + 0.00000000e+00j,
+                      2.00947715e-09 - 9.84327394e-25j])
+        y = wavelets.morlet(3, w=2, complete=False)
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, s=4, complete=True)
+        y = wavelets.morlet(20000, s=8, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, s=4, complete=False)
+        assert_array_almost_equal(y, x, decimal=2)
+        y = wavelets.morlet(20000, s=8, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=3, s=5, complete=True)
+        y = wavelets.morlet(20000, w=3, s=10, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=3, s=5, complete=False)
+        assert_array_almost_equal(y, x, decimal=2)
+        y = wavelets.morlet(20000, w=3, s=10, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=7, s=10, complete=True)
+        y = wavelets.morlet(20000, w=7, s=20, complete=True)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+        x = wavelets.morlet(10000, w=7, s=10, complete=False)
+        assert_array_almost_equal(x, y, decimal=2)
+        y = wavelets.morlet(20000, w=7, s=20, complete=False)[5000:15000]
+        assert_array_almost_equal(x, y, decimal=2)
+
+    def test_morlet2(self):
+        w = wavelets.morlet2(1.0, 0.5)
+        expected = (np.pi**(-0.25) * np.sqrt(1/0.5)).astype(complex)
+        assert_array_equal(w, expected)
+
+        lengths = [5, 11, 15, 51, 101]
+        for length in lengths:
+            w = wavelets.morlet2(length, 1.0)
+            assert_(len(w) == length)
+            max_loc = np.argmax(w)
+            assert_(max_loc == (length // 2))
+
+        points = 100
+        w = abs(wavelets.morlet2(points, 2.0))
+        half_vec = np.arange(0, points // 2)
+        assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
+
+        x = np.array([5.03701224e-09 + 2.46742437e-24j,
+                      1.88279253e+00 + 0.00000000e+00j,
+                      5.03701224e-09 - 2.46742437e-24j])
+        y = wavelets.morlet2(3, s=1/(2*np.pi), w=2)
+        assert_array_almost_equal(x, y)
+
+    def test_ricker(self):
+        w = wavelets.ricker(1.0, 1)
+        expected = 2 / (np.sqrt(3 * 1.0) * (np.pi ** 0.25))
+        assert_array_equal(w, expected)
+
+        lengths = [5, 11, 15, 51, 101]
+        for length in lengths:
+            w = wavelets.ricker(length, 1.0)
+            assert_(len(w) == length)
+            max_loc = np.argmax(w)
+            assert_(max_loc == (length // 2))
+
+        points = 100
+        w = wavelets.ricker(points, 2.0)
+        half_vec = np.arange(0, points // 2)
+        #Wavelet should be symmetric
+        assert_array_almost_equal(w[half_vec], w[-(half_vec + 1)])
+
+        #Check zeros
+        aas = [5, 10, 15, 20, 30]
+        points = 99
+        for a in aas:
+            w = wavelets.ricker(points, a)
+            vec = np.arange(0, points) - (points - 1.0) / 2
+            exp_zero1 = np.argmin(np.abs(vec - a))
+            exp_zero2 = np.argmin(np.abs(vec + a))
+            assert_array_almost_equal(w[exp_zero1], 0)
+            assert_array_almost_equal(w[exp_zero2], 0)
+
+    def test_cwt(self):
+        widths = [1.0]
+        delta_wavelet = lambda s, t: np.array([1])
+        len_data = 100
+        test_data = np.sin(np.pi * np.arange(0, len_data) / 10.0)
+
+        #Test delta function input gives same data as output
+        cwt_dat = wavelets.cwt(test_data, delta_wavelet, widths)
+        assert_(cwt_dat.shape == (len(widths), len_data))
+        assert_array_almost_equal(test_data, cwt_dat.flatten())
+
+        #Check proper shape on output
+        widths = [1, 3, 4, 5, 10]
+        cwt_dat = wavelets.cwt(test_data, wavelets.ricker, widths)
+        assert_(cwt_dat.shape == (len(widths), len_data))
+
+        widths = [len_data * 10]
+        #Note: this wavelet isn't defined quite right, but is fine for this test
+        flat_wavelet = lambda l, w: np.full(w, 1 / w)
+        cwt_dat = wavelets.cwt(test_data, flat_wavelet, widths)
+        assert_array_almost_equal(cwt_dat, np.mean(test_data))
+

venv/Lib/site-packages/scipy/signal/waveforms.py

@@ -0,0 +1,664 @@
+# Author: Travis Oliphant
+# 2003
+#
+# Feb. 2010: Updated by Warren Weckesser:
+#   Rewrote much of chirp()
+#   Added sweep_poly()
+import numpy as np
+from numpy import asarray, zeros, place, nan, mod, pi, extract, log, sqrt, \
+    exp, cos, sin, polyval, polyint
+
+
+__all__ = ['sawtooth', 'square', 'gausspulse', 'chirp', 'sweep_poly',
+           'unit_impulse']
+
+
+def sawtooth(t, width=1):
+    """
+    Return a periodic sawtooth or triangle waveform.
+
+    The sawtooth waveform has a period ``2*pi``, rises from -1 to 1 on the
+    interval 0 to ``width*2*pi``, then drops from 1 to -1 on the interval
+    ``width*2*pi`` to ``2*pi``. `width` must be in the interval [0, 1].
+
+    Note that this is not band-limited.  It produces an infinite number
+    of harmonics, which are aliased back and forth across the frequency
+    spectrum.
+
+    Parameters
+    ----------
+    t : array_like
+        Time.
+    width : array_like, optional
+        Width of the rising ramp as a proportion of the total cycle.
+        Default is 1, producing a rising ramp, while 0 produces a falling
+        ramp.  `width` = 0.5 produces a triangle wave.
+        If an array, causes wave shape to change over time, and must be the
+        same length as t.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing the sawtooth waveform.
+
+    Examples
+    --------
+    A 5 Hz waveform sampled at 500 Hz for 1 second:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(0, 1, 500)
+    >>> plt.plot(t, signal.sawtooth(2 * np.pi * 5 * t))
+
+    """
+    t, w = asarray(t), asarray(width)
+    w = asarray(w + (t - t))
+    t = asarray(t + (w - w))
+    if t.dtype.char in ['fFdD']:
+        ytype = t.dtype.char
+    else:
+        ytype = 'd'
+    y = zeros(t.shape, ytype)
+
+    # width must be between 0 and 1 inclusive
+    mask1 = (w > 1) | (w < 0)
+    place(y, mask1, nan)
+
+    # take t modulo 2*pi
+    tmod = mod(t, 2 * pi)
+
+    # on the interval 0 to width*2*pi function is
+    #  tmod / (pi*w) - 1
+    mask2 = (1 - mask1) & (tmod < w * 2 * pi)
+    tsub = extract(mask2, tmod)
+    wsub = extract(mask2, w)
+    place(y, mask2, tsub / (pi * wsub) - 1)
+
+    # on the interval width*2*pi to 2*pi function is
+    #  (pi*(w+1)-tmod) / (pi*(1-w))
+
+    mask3 = (1 - mask1) & (1 - mask2)
+    tsub = extract(mask3, tmod)
+    wsub = extract(mask3, w)
+    place(y, mask3, (pi * (wsub + 1) - tsub) / (pi * (1 - wsub)))
+    return y
+
+
+def square(t, duty=0.5):
+    """
+    Return a periodic square-wave waveform.
+
+    The square wave has a period ``2*pi``, has value +1 from 0 to
+    ``2*pi*duty`` and -1 from ``2*pi*duty`` to ``2*pi``. `duty` must be in
+    the interval [0,1].
+
+    Note that this is not band-limited.  It produces an infinite number
+    of harmonics, which are aliased back and forth across the frequency
+    spectrum.
+
+    Parameters
+    ----------
+    t : array_like
+        The input time array.
+    duty : array_like, optional
+        Duty cycle.  Default is 0.5 (50% duty cycle).
+        If an array, causes wave shape to change over time, and must be the
+        same length as t.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing the square waveform.
+
+    Examples
+    --------
+    A 5 Hz waveform sampled at 500 Hz for 1 second:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(0, 1, 500, endpoint=False)
+    >>> plt.plot(t, signal.square(2 * np.pi * 5 * t))
+    >>> plt.ylim(-2, 2)
+
+    A pulse-width modulated sine wave:
+
+    >>> plt.figure()
+    >>> sig = np.sin(2 * np.pi * t)
+    >>> pwm = signal.square(2 * np.pi * 30 * t, duty=(sig + 1)/2)
+    >>> plt.subplot(2, 1, 1)
+    >>> plt.plot(t, sig)
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(t, pwm)
+    >>> plt.ylim(-1.5, 1.5)
+
+    """
+    t, w = asarray(t), asarray(duty)
+    w = asarray(w + (t - t))
+    t = asarray(t + (w - w))
+    if t.dtype.char in ['fFdD']:
+        ytype = t.dtype.char
+    else:
+        ytype = 'd'
+
+    y = zeros(t.shape, ytype)
+
+    # width must be between 0 and 1 inclusive
+    mask1 = (w > 1) | (w < 0)
+    place(y, mask1, nan)
+
+    # on the interval 0 to duty*2*pi function is 1
+    tmod = mod(t, 2 * pi)
+    mask2 = (1 - mask1) & (tmod < w * 2 * pi)
+    place(y, mask2, 1)
+
+    # on the interval duty*2*pi to 2*pi function is
+    #  (pi*(w+1)-tmod) / (pi*(1-w))
+    mask3 = (1 - mask1) & (1 - mask2)
+    place(y, mask3, -1)
+    return y
+
+
+def gausspulse(t, fc=1000, bw=0.5, bwr=-6, tpr=-60, retquad=False,
+               retenv=False):
+    """
+    Return a Gaussian modulated sinusoid:
+
+        ``exp(-a t^2) exp(1j*2*pi*fc*t).``
+
+    If `retquad` is True, then return the real and imaginary parts
+    (in-phase and quadrature).
+    If `retenv` is True, then return the envelope (unmodulated signal).
+    Otherwise, return the real part of the modulated sinusoid.
+
+    Parameters
+    ----------
+    t : ndarray or the string 'cutoff'
+        Input array.
+    fc : float, optional
+        Center frequency (e.g. Hz).  Default is 1000.
+    bw : float, optional
+        Fractional bandwidth in frequency domain of pulse (e.g. Hz).
+        Default is 0.5.
+    bwr : float, optional
+        Reference level at which fractional bandwidth is calculated (dB).
+        Default is -6.
+    tpr : float, optional
+        If `t` is 'cutoff', then the function returns the cutoff
+        time for when the pulse amplitude falls below `tpr` (in dB).
+        Default is -60.
+    retquad : bool, optional
+        If True, return the quadrature (imaginary) as well as the real part
+        of the signal.  Default is False.
+    retenv : bool, optional
+        If True, return the envelope of the signal.  Default is False.
+
+    Returns
+    -------
+    yI : ndarray
+        Real part of signal.  Always returned.
+    yQ : ndarray
+        Imaginary part of signal.  Only returned if `retquad` is True.
+    yenv : ndarray
+        Envelope of signal.  Only returned if `retenv` is True.
+
+    See Also
+    --------
+    scipy.signal.morlet
+
+    Examples
+    --------
+    Plot real component, imaginary component, and envelope for a 5 Hz pulse,
+    sampled at 100 Hz for 2 seconds:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(-1, 1, 2 * 100, endpoint=False)
+    >>> i, q, e = signal.gausspulse(t, fc=5, retquad=True, retenv=True)
+    >>> plt.plot(t, i, t, q, t, e, '--')
+
+    """
+    if fc < 0:
+        raise ValueError("Center frequency (fc=%.2f) must be >=0." % fc)
+    if bw <= 0:
+        raise ValueError("Fractional bandwidth (bw=%.2f) must be > 0." % bw)
+    if bwr >= 0:
+        raise ValueError("Reference level for bandwidth (bwr=%.2f) must "
+                         "be < 0 dB" % bwr)
+
+    # exp(-a t^2) <->  sqrt(pi/a) exp(-pi^2/a * f^2)  = g(f)
+
+    ref = pow(10.0, bwr / 20.0)
+    # fdel = fc*bw/2:  g(fdel) = ref --- solve this for a
+    #
+    # pi^2/a * fc^2 * bw^2 /4=-log(ref)
+    a = -(pi * fc * bw) ** 2 / (4.0 * log(ref))
+
+    if isinstance(t, str):
+        if t == 'cutoff':  # compute cut_off point
+            #  Solve exp(-a tc**2) = tref  for tc
+            #   tc = sqrt(-log(tref) / a) where tref = 10^(tpr/20)
+            if tpr >= 0:
+                raise ValueError("Reference level for time cutoff must "
+                                 "be < 0 dB")
+            tref = pow(10.0, tpr / 20.0)
+            return sqrt(-log(tref) / a)
+        else:
+            raise ValueError("If `t` is a string, it must be 'cutoff'")
+
+    yenv = exp(-a * t * t)
+    yI = yenv * cos(2 * pi * fc * t)
+    yQ = yenv * sin(2 * pi * fc * t)
+    if not retquad and not retenv:
+        return yI
+    if not retquad and retenv:
+        return yI, yenv
+    if retquad and not retenv:
+        return yI, yQ
+    if retquad and retenv:
+        return yI, yQ, yenv
+
+
+def chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True):
+    """Frequency-swept cosine generator.
+
+    In the following, 'Hz' should be interpreted as 'cycles per unit';
+    there is no requirement here that the unit is one second.  The
+    important distinction is that the units of rotation are cycles, not
+    radians. Likewise, `t` could be a measurement of space instead of time.
+
+    Parameters
+    ----------
+    t : array_like
+        Times at which to evaluate the waveform.
+    f0 : float
+        Frequency (e.g. Hz) at time t=0.
+    t1 : float
+        Time at which `f1` is specified.
+    f1 : float
+        Frequency (e.g. Hz) of the waveform at time `t1`.
+    method : {'linear', 'quadratic', 'logarithmic', 'hyperbolic'}, optional
+        Kind of frequency sweep.  If not given, `linear` is assumed.  See
+        Notes below for more details.
+    phi : float, optional
+        Phase offset, in degrees. Default is 0.
+    vertex_zero : bool, optional
+        This parameter is only used when `method` is 'quadratic'.
+        It determines whether the vertex of the parabola that is the graph
+        of the frequency is at t=0 or t=t1.
+
+    Returns
+    -------
+    y : ndarray
+        A numpy array containing the signal evaluated at `t` with the
+        requested time-varying frequency.  More precisely, the function
+        returns ``cos(phase + (pi/180)*phi)`` where `phase` is the integral
+        (from 0 to `t`) of ``2*pi*f(t)``. ``f(t)`` is defined below.
+
+    See Also
+    --------
+    sweep_poly
+
+    Notes
+    -----
+    There are four options for the `method`.  The following formulas give
+    the instantaneous frequency (in Hz) of the signal generated by
+    `chirp()`.  For convenience, the shorter names shown below may also be
+    used.
+
+    linear, lin, li:
+
+        ``f(t) = f0 + (f1 - f0) * t / t1``
+
+    quadratic, quad, q:
+
+        The graph of the frequency f(t) is a parabola through (0, f0) and
+        (t1, f1).  By default, the vertex of the parabola is at (0, f0).
+        If `vertex_zero` is False, then the vertex is at (t1, f1).  The
+        formula is:
+
+        if vertex_zero is True:
+
+            ``f(t) = f0 + (f1 - f0) * t**2 / t1**2``
+
+        else:
+
+            ``f(t) = f1 - (f1 - f0) * (t1 - t)**2 / t1**2``
+
+        To use a more general quadratic function, or an arbitrary
+        polynomial, use the function `scipy.signal.sweep_poly`.
+
+    logarithmic, log, lo:
+
+        ``f(t) = f0 * (f1/f0)**(t/t1)``
+
+        f0 and f1 must be nonzero and have the same sign.
+
+        This signal is also known as a geometric or exponential chirp.
+
+    hyperbolic, hyp:
+
+        ``f(t) = f0*f1*t1 / ((f0 - f1)*t + f1*t1)``
+
+        f0 and f1 must be nonzero.
+
+    Examples
+    --------
+    The following will be used in the examples:
+
+    >>> from scipy.signal import chirp, spectrogram
+    >>> import matplotlib.pyplot as plt
+
+    For the first example, we'll plot the waveform for a linear chirp
+    from 6 Hz to 1 Hz over 10 seconds:
+
+    >>> t = np.linspace(0, 10, 1500)
+    >>> w = chirp(t, f0=6, f1=1, t1=10, method='linear')
+    >>> plt.plot(t, w)
+    >>> plt.title("Linear Chirp, f(0)=6, f(10)=1")
+    >>> plt.xlabel('t (sec)')
+    >>> plt.show()
+
+    For the remaining examples, we'll use higher frequency ranges,
+    and demonstrate the result using `scipy.signal.spectrogram`.
+    We'll use a 4 second interval sampled at 7200 Hz.
+
+    >>> fs = 7200
+    >>> T = 4
+    >>> t = np.arange(0, int(T*fs)) / fs
+
+    We'll use this function to plot the spectrogram in each example.
+
+    >>> def plot_spectrogram(title, w, fs):
+    ...     ff, tt, Sxx = spectrogram(w, fs=fs, nperseg=256, nfft=576)
+    ...     plt.pcolormesh(tt, ff[:145], Sxx[:145], cmap='gray_r', shading='gouraud')
+    ...     plt.title(title)
+    ...     plt.xlabel('t (sec)')
+    ...     plt.ylabel('Frequency (Hz)')
+    ...     plt.grid()
+    ...
+
+    Quadratic chirp from 1500 Hz to 250 Hz
+    (vertex of the parabolic curve of the frequency is at t=0):
+
+    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='quadratic')
+    >>> plot_spectrogram(f'Quadratic Chirp, f(0)=1500, f({T})=250', w, fs)
+    >>> plt.show()
+
+    Quadratic chirp from 1500 Hz to 250 Hz
+    (vertex of the parabolic curve of the frequency is at t=T):
+
+    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='quadratic',
+    ...           vertex_zero=False)
+    >>> plot_spectrogram(f'Quadratic Chirp, f(0)=1500, f({T})=250\\n' +
+    ...                  '(vertex_zero=False)', w, fs)
+    >>> plt.show()
+
+    Logarithmic chirp from 1500 Hz to 250 Hz:
+
+    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='logarithmic')
+    >>> plot_spectrogram(f'Logarithmic Chirp, f(0)=1500, f({T})=250', w, fs)
+    >>> plt.show()
+
+    Hyperbolic chirp from 1500 Hz to 250 Hz:
+
+    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='hyperbolic')
+    >>> plot_spectrogram(f'Hyperbolic Chirp, f(0)=1500, f({T})=250', w, fs)
+    >>> plt.show()
+
+    """
+    # 'phase' is computed in _chirp_phase, to make testing easier.
+    phase = _chirp_phase(t, f0, t1, f1, method, vertex_zero)
+    # Convert  phi to radians.
+    phi *= pi / 180
+    return cos(phase + phi)
+
+
+def _chirp_phase(t, f0, t1, f1, method='linear', vertex_zero=True):
+    """
+    Calculate the phase used by `chirp` to generate its output.
+
+    See `chirp` for a description of the arguments.
+
+    """
+    t = asarray(t)
+    f0 = float(f0)
+    t1 = float(t1)
+    f1 = float(f1)
+    if method in ['linear', 'lin', 'li']:
+        beta = (f1 - f0) / t1
+        phase = 2 * pi * (f0 * t + 0.5 * beta * t * t)
+
+    elif method in ['quadratic', 'quad', 'q']:
+        beta = (f1 - f0) / (t1 ** 2)
+        if vertex_zero:
+            phase = 2 * pi * (f0 * t + beta * t ** 3 / 3)
+        else:
+            phase = 2 * pi * (f1 * t + beta * ((t1 - t) ** 3 - t1 ** 3) / 3)
+
+    elif method in ['logarithmic', 'log', 'lo']:
+        if f0 * f1 <= 0.0:
+            raise ValueError("For a logarithmic chirp, f0 and f1 must be "
+                             "nonzero and have the same sign.")
+        if f0 == f1:
+            phase = 2 * pi * f0 * t
+        else:
+            beta = t1 / log(f1 / f0)
+            phase = 2 * pi * beta * f0 * (pow(f1 / f0, t / t1) - 1.0)
+
+    elif method in ['hyperbolic', 'hyp']:
+        if f0 == 0 or f1 == 0:
+            raise ValueError("For a hyperbolic chirp, f0 and f1 must be "
+                             "nonzero.")
+        if f0 == f1:
+            # Degenerate case: constant frequency.
+            phase = 2 * pi * f0 * t
+        else:
+            # Singular point: the instantaneous frequency blows up
+            # when t == sing.
+            sing = -f1 * t1 / (f0 - f1)
+            phase = 2 * pi * (-sing * f0) * log(np.abs(1 - t/sing))
+
+    else:
+        raise ValueError("method must be 'linear', 'quadratic', 'logarithmic',"
+                         " or 'hyperbolic', but a value of %r was given."
+                         % method)
+
+    return phase
+
+
+def sweep_poly(t, poly, phi=0):
+    """
+    Frequency-swept cosine generator, with a time-dependent frequency.
+
+    This function generates a sinusoidal function whose instantaneous
+    frequency varies with time.  The frequency at time `t` is given by
+    the polynomial `poly`.
+
+    Parameters
+    ----------
+    t : ndarray
+        Times at which to evaluate the waveform.
+    poly : 1-D array_like or instance of numpy.poly1d
+        The desired frequency expressed as a polynomial.  If `poly` is
+        a list or ndarray of length n, then the elements of `poly` are
+        the coefficients of the polynomial, and the instantaneous
+        frequency is
+
+          ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]``
+
+        If `poly` is an instance of numpy.poly1d, then the
+        instantaneous frequency is
+
+          ``f(t) = poly(t)``
+
+    phi : float, optional
+        Phase offset, in degrees, Default: 0.
+
+    Returns
+    -------
+    sweep_poly : ndarray
+        A numpy array containing the signal evaluated at `t` with the
+        requested time-varying frequency.  More precisely, the function
+        returns ``cos(phase + (pi/180)*phi)``, where `phase` is the integral
+        (from 0 to t) of ``2 * pi * f(t)``; ``f(t)`` is defined above.
+
+    See Also
+    --------
+    chirp
+
+    Notes
+    -----
+    .. versionadded:: 0.8.0
+
+    If `poly` is a list or ndarray of length `n`, then the elements of
+    `poly` are the coefficients of the polynomial, and the instantaneous
+    frequency is:
+
+        ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]``
+
+    If `poly` is an instance of `numpy.poly1d`, then the instantaneous
+    frequency is:
+
+          ``f(t) = poly(t)``
+
+    Finally, the output `s` is:
+
+        ``cos(phase + (pi/180)*phi)``
+
+    where `phase` is the integral from 0 to `t` of ``2 * pi * f(t)``,
+    ``f(t)`` as defined above.
+
+    Examples
+    --------
+    Compute the waveform with instantaneous frequency::
+
+        f(t) = 0.025*t**3 - 0.36*t**2 + 1.25*t + 2
+
+    over the interval 0 <= t <= 10.
+
+    >>> from scipy.signal import sweep_poly
+    >>> p = np.poly1d([0.025, -0.36, 1.25, 2.0])
+    >>> t = np.linspace(0, 10, 5001)
+    >>> w = sweep_poly(t, p)
+
+    Plot it:
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.subplot(2, 1, 1)
+    >>> plt.plot(t, w)
+    >>> plt.title("Sweep Poly\\nwith frequency " +
+    ...           "$f(t) = 0.025t^3 - 0.36t^2 + 1.25t + 2$")
+    >>> plt.subplot(2, 1, 2)
+    >>> plt.plot(t, p(t), 'r', label='f(t)')
+    >>> plt.legend()
+    >>> plt.xlabel('t')
+    >>> plt.tight_layout()
+    >>> plt.show()
+
+    """
+    # 'phase' is computed in _sweep_poly_phase, to make testing easier.
+    phase = _sweep_poly_phase(t, poly)
+    # Convert to radians.
+    phi *= pi / 180
+    return cos(phase + phi)
+
+
+def _sweep_poly_phase(t, poly):
+    """
+    Calculate the phase used by sweep_poly to generate its output.
+
+    See `sweep_poly` for a description of the arguments.
+
+    """
+    # polyint handles lists, ndarrays and instances of poly1d automatically.
+    intpoly = polyint(poly)
+    phase = 2 * pi * polyval(intpoly, t)
+    return phase
+
+
+def unit_impulse(shape, idx=None, dtype=float):
+    """
+    Unit impulse signal (discrete delta function) or unit basis vector.
+
+    Parameters
+    ----------
+    shape : int or tuple of int
+        Number of samples in the output (1-D), or a tuple that represents the
+        shape of the output (N-D).
+    idx : None or int or tuple of int or 'mid', optional
+        Index at which the value is 1.  If None, defaults to the 0th element.
+        If ``idx='mid'``, the impulse will be centered at ``shape // 2`` in
+        all dimensions.  If an int, the impulse will be at `idx` in all
+        dimensions.
+    dtype : data-type, optional
+        The desired data-type for the array, e.g., ``numpy.int8``.  Default is
+        ``numpy.float64``.
+
+    Returns
+    -------
+    y : ndarray
+        Output array containing an impulse signal.
+
+    Notes
+    -----
+    The 1D case is also known as the Kronecker delta.
+
+    .. versionadded:: 0.19.0
+
+    Examples
+    --------
+    An impulse at the 0th element (:math:`\\delta[n]`):
+
+    >>> from scipy import signal
+    >>> signal.unit_impulse(8)
+    array([ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])
+
+    Impulse offset by 2 samples (:math:`\\delta[n-2]`):
+
+    >>> signal.unit_impulse(7, 2)
+    array([ 0.,  0.,  1.,  0.,  0.,  0.,  0.])
+
+    2-dimensional impulse, centered:
+
+    >>> signal.unit_impulse((3, 3), 'mid')
+    array([[ 0.,  0.,  0.],
+           [ 0.,  1.,  0.],
+           [ 0.,  0.,  0.]])
+
+    Impulse at (2, 2), using broadcasting:
+
+    >>> signal.unit_impulse((4, 4), 2)
+    array([[ 0.,  0.,  0.,  0.],
+           [ 0.,  0.,  0.,  0.],
+           [ 0.,  0.,  1.,  0.],
+           [ 0.,  0.,  0.,  0.]])
+
+    Plot the impulse response of a 4th-order Butterworth lowpass filter:
+
+    >>> imp = signal.unit_impulse(100, 'mid')
+    >>> b, a = signal.butter(4, 0.2)
+    >>> response = signal.lfilter(b, a, imp)
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(np.arange(-50, 50), imp)
+    >>> plt.plot(np.arange(-50, 50), response)
+    >>> plt.margins(0.1, 0.1)
+    >>> plt.xlabel('Time [samples]')
+    >>> plt.ylabel('Amplitude')
+    >>> plt.grid(True)
+    >>> plt.show()
+
+    """
+    out = zeros(shape, dtype)
+
+    shape = np.atleast_1d(shape)
+
+    if idx is None:
+        idx = (0,) * len(shape)
+    elif idx == 'mid':
+        idx = tuple(shape // 2)
+    elif not hasattr(idx, "__iter__"):
+        idx = (idx,) * len(shape)
+
+    out[idx] = 1
+    return out

venv/Lib/site-packages/scipy/signal/wavelets.py

@@ -0,0 +1,481 @@
+import numpy as np
+from scipy.linalg import eig
+from scipy.special import comb
+from scipy.signal import convolve
+
+__all__ = ['daub', 'qmf', 'cascade', 'morlet', 'ricker', 'morlet2', 'cwt']
+
+
+def daub(p):
+    """
+    The coefficients for the FIR low-pass filter producing Daubechies wavelets.
+
+    p>=1 gives the order of the zero at f=1/2.
+    There are 2p filter coefficients.
+
+    Parameters
+    ----------
+    p : int
+        Order of the zero at f=1/2, can have values from 1 to 34.
+
+    Returns
+    -------
+    daub : ndarray
+        Return
+
+    """
+    sqrt = np.sqrt
+    if p < 1:
+        raise ValueError("p must be at least 1.")
+    if p == 1:
+        c = 1 / sqrt(2)
+        return np.array([c, c])
+    elif p == 2:
+        f = sqrt(2) / 8
+        c = sqrt(3)
+        return f * np.array([1 + c, 3 + c, 3 - c, 1 - c])
+    elif p == 3:
+        tmp = 12 * sqrt(10)
+        z1 = 1.5 + sqrt(15 + tmp) / 6 - 1j * (sqrt(15) + sqrt(tmp - 15)) / 6
+        z1c = np.conj(z1)
+        f = sqrt(2) / 8
+        d0 = np.real((1 - z1) * (1 - z1c))
+        a0 = np.real(z1 * z1c)
+        a1 = 2 * np.real(z1)
+        return f / d0 * np.array([a0, 3 * a0 - a1, 3 * a0 - 3 * a1 + 1,
+                                  a0 - 3 * a1 + 3, 3 - a1, 1])
+    elif p < 35:
+        # construct polynomial and factor it
+        if p < 35:
+            P = [comb(p - 1 + k, k, exact=1) for k in range(p)][::-1]
+            yj = np.roots(P)
+        else:  # try different polynomial --- needs work
+            P = [comb(p - 1 + k, k, exact=1) / 4.0**k
+                 for k in range(p)][::-1]
+            yj = np.roots(P) / 4
+        # for each root, compute two z roots, select the one with |z|>1
+        # Build up final polynomial
+        c = np.poly1d([1, 1])**p
+        q = np.poly1d([1])
+        for k in range(p - 1):
+            yval = yj[k]
+            part = 2 * sqrt(yval * (yval - 1))
+            const = 1 - 2 * yval
+            z1 = const + part
+            if (abs(z1)) < 1:
+                z1 = const - part
+            q = q * [1, -z1]
+
+        q = c * np.real(q)
+        # Normalize result
+        q = q / np.sum(q) * sqrt(2)
+        return q.c[::-1]
+    else:
+        raise ValueError("Polynomial factorization does not work "
+                         "well for p too large.")
+
+
+def qmf(hk):
+    """
+    Return high-pass qmf filter from low-pass
+
+    Parameters
+    ----------
+    hk : array_like
+        Coefficients of high-pass filter.
+
+    """
+    N = len(hk) - 1
+    asgn = [{0: 1, 1: -1}[k % 2] for k in range(N + 1)]
+    return hk[::-1] * np.array(asgn)
+
+
+def cascade(hk, J=7):
+    """
+    Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients.
+
+    Parameters
+    ----------
+    hk : array_like
+        Coefficients of low-pass filter.
+    J : int, optional
+        Values will be computed at grid points ``K/2**J``. Default is 7.
+
+    Returns
+    -------
+    x : ndarray
+        The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where
+        ``len(hk) = len(gk) = N+1``.
+    phi : ndarray
+        The scaling function ``phi(x)`` at `x`:
+        ``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N.
+    psi : ndarray, optional
+        The wavelet function ``psi(x)`` at `x`:
+        ``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N.
+        `psi` is only returned if `gk` is not None.
+
+    Notes
+    -----
+    The algorithm uses the vector cascade algorithm described by Strang and
+    Nguyen in "Wavelets and Filter Banks".  It builds a dictionary of values
+    and slices for quick reuse.  Then inserts vectors into final vector at the
+    end.
+
+    """
+    N = len(hk) - 1
+
+    if (J > 30 - np.log2(N + 1)):
+        raise ValueError("Too many levels.")
+    if (J < 1):
+        raise ValueError("Too few levels.")
+
+    # construct matrices needed
+    nn, kk = np.ogrid[:N, :N]
+    s2 = np.sqrt(2)
+    # append a zero so that take works
+    thk = np.r_[hk, 0]
+    gk = qmf(hk)
+    tgk = np.r_[gk, 0]
+
+    indx1 = np.clip(2 * nn - kk, -1, N + 1)
+    indx2 = np.clip(2 * nn - kk + 1, -1, N + 1)
+    m = np.zeros((2, 2, N, N), 'd')
+    m[0, 0] = np.take(thk, indx1, 0)
+    m[0, 1] = np.take(thk, indx2, 0)
+    m[1, 0] = np.take(tgk, indx1, 0)
+    m[1, 1] = np.take(tgk, indx2, 0)
+    m *= s2
+
+    # construct the grid of points
+    x = np.arange(0, N * (1 << J), dtype=float) / (1 << J)
+    phi = 0 * x
+
+    psi = 0 * x
+
+    # find phi0, and phi1
+    lam, v = eig(m[0, 0])
+    ind = np.argmin(np.absolute(lam - 1))
+    # a dictionary with a binary representation of the
+    #   evaluation points x < 1 -- i.e. position is 0.xxxx
+    v = np.real(v[:, ind])
+    # need scaling function to integrate to 1 so find
+    #  eigenvector normalized to sum(v,axis=0)=1
+    sm = np.sum(v)
+    if sm < 0:  # need scaling function to integrate to 1
+        v = -v
+        sm = -sm
+    bitdic = {'0': v / sm}
+    bitdic['1'] = np.dot(m[0, 1], bitdic['0'])
+    step = 1 << J
+    phi[::step] = bitdic['0']
+    phi[(1 << (J - 1))::step] = bitdic['1']
+    psi[::step] = np.dot(m[1, 0], bitdic['0'])
+    psi[(1 << (J - 1))::step] = np.dot(m[1, 1], bitdic['0'])
+    # descend down the levels inserting more and more values
+    #  into bitdic -- store the values in the correct location once we
+    #  have computed them -- stored in the dictionary
+    #  for quicker use later.
+    prevkeys = ['1']
+    for level in range(2, J + 1):
+        newkeys = ['%d%s' % (xx, yy) for xx in [0, 1] for yy in prevkeys]
+        fac = 1 << (J - level)
+        for key in newkeys:
+            # convert key to number
+            num = 0
+            for pos in range(level):
+                if key[pos] == '1':
+                    num += (1 << (level - 1 - pos))
+            pastphi = bitdic[key[1:]]
+            ii = int(key[0])
+            temp = np.dot(m[0, ii], pastphi)
+            bitdic[key] = temp
+            phi[num * fac::step] = temp
+            psi[num * fac::step] = np.dot(m[1, ii], pastphi)
+        prevkeys = newkeys
+
+    return x, phi, psi
+
+
+def morlet(M, w=5.0, s=1.0, complete=True):
+    """
+    Complex Morlet wavelet.
+
+    Parameters
+    ----------
+    M : int
+        Length of the wavelet.
+    w : float, optional
+        Omega0. Default is 5
+    s : float, optional
+        Scaling factor, windowed from ``-s*2*pi`` to ``+s*2*pi``. Default is 1.
+    complete : bool, optional
+        Whether to use the complete or the standard version.
+
+    Returns
+    -------
+    morlet : (M,) ndarray
+
+    See Also
+    --------
+    morlet2 : Implementation of Morlet wavelet, compatible with `cwt`.
+    scipy.signal.gausspulse
+
+    Notes
+    -----
+    The standard version::
+
+        pi**-0.25 * exp(1j*w*x) * exp(-0.5*(x**2))
+
+    This commonly used wavelet is often referred to simply as the
+    Morlet wavelet.  Note that this simplified version can cause
+    admissibility problems at low values of `w`.
+
+    The complete version::
+
+        pi**-0.25 * (exp(1j*w*x) - exp(-0.5*(w**2))) * exp(-0.5*(x**2))
+
+    This version has a correction
+    term to improve admissibility. For `w` greater than 5, the
+    correction term is negligible.
+
+    Note that the energy of the return wavelet is not normalised
+    according to `s`.
+
+    The fundamental frequency of this wavelet in Hz is given
+    by ``f = 2*s*w*r / M`` where `r` is the sampling rate.
+
+    Note: This function was created before `cwt` and is not compatible
+    with it.
+
+    """
+    x = np.linspace(-s * 2 * np.pi, s * 2 * np.pi, M)
+    output = np.exp(1j * w * x)
+
+    if complete:
+        output -= np.exp(-0.5 * (w**2))
+
+    output *= np.exp(-0.5 * (x**2)) * np.pi**(-0.25)
+
+    return output
+
+
+def ricker(points, a):
+    """
+    Return a Ricker wavelet, also known as the "Mexican hat wavelet".
+
+    It models the function:
+
+        ``A * (1 - (x/a)**2) * exp(-0.5*(x/a)**2)``,
+
+    where ``A = 2/(sqrt(3*a)*(pi**0.25))``.
+
+    Parameters
+    ----------
+    points : int
+        Number of points in `vector`.
+        Will be centered around 0.
+    a : scalar
+        Width parameter of the wavelet.
+
+    Returns
+    -------
+    vector : (N,) ndarray
+        Array of length `points` in shape of ricker curve.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> points = 100
+    >>> a = 4.0
+    >>> vec2 = signal.ricker(points, a)
+    >>> print(len(vec2))
+    100
+    >>> plt.plot(vec2)
+    >>> plt.show()
+
+    """
+    A = 2 / (np.sqrt(3 * a) * (np.pi**0.25))
+    wsq = a**2
+    vec = np.arange(0, points) - (points - 1.0) / 2
+    xsq = vec**2
+    mod = (1 - xsq / wsq)
+    gauss = np.exp(-xsq / (2 * wsq))
+    total = A * mod * gauss
+    return total
+
+
+def morlet2(M, s, w=5):
+    """
+    Complex Morlet wavelet, designed to work with `cwt`.
+
+    Returns the complete version of morlet wavelet, normalised
+    according to `s`::
+
+        exp(1j*w*x/s) * exp(-0.5*(x/s)**2) * pi**(-0.25) * sqrt(1/s)
+
+    Parameters
+    ----------
+    M : int
+        Length of the wavelet.
+    s : float
+        Width parameter of the wavelet.
+    w : float, optional
+        Omega0. Default is 5
+
+    Returns
+    -------
+    morlet : (M,) ndarray
+
+    See Also
+    --------
+    morlet : Implementation of Morlet wavelet, incompatible with `cwt`
+
+    Notes
+    -----
+
+    .. versionadded:: 1.4.0
+
+    This function was designed to work with `cwt`. Because `morlet2`
+    returns an array of complex numbers, the `dtype` argument of `cwt`
+    should be set to `complex128` for best results.
+
+    Note the difference in implementation with `morlet`.
+    The fundamental frequency of this wavelet in Hz is given by::
+
+        f = w*fs / (2*s*np.pi)
+
+    where ``fs`` is the sampling rate and `s` is the wavelet width parameter.
+    Similarly we can get the wavelet width parameter at ``f``::
+
+        s = w*fs / (2*f*np.pi)
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+
+    >>> M = 100
+    >>> s = 4.0
+    >>> w = 2.0
+    >>> wavelet = signal.morlet2(M, s, w)
+    >>> plt.plot(abs(wavelet))
+    >>> plt.show()
+
+    This example shows basic use of `morlet2` with `cwt` in time-frequency
+    analysis:
+
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t, dt = np.linspace(0, 1, 200, retstep=True)
+    >>> fs = 1/dt
+    >>> w = 6.
+    >>> sig = np.cos(2*np.pi*(50 + 10*t)*t) + np.sin(40*np.pi*t)
+    >>> freq = np.linspace(1, fs/2, 100)
+    >>> widths = w*fs / (2*freq*np.pi)
+    >>> cwtm = signal.cwt(sig, signal.morlet2, widths, w=w)
+    >>> plt.pcolormesh(t, freq, np.abs(cwtm), cmap='viridis', shading='gouraud')
+    >>> plt.show()
+
+    """
+    x = np.arange(0, M) - (M - 1.0) / 2
+    x = x / s
+    wavelet = np.exp(1j * w * x) * np.exp(-0.5 * x**2) * np.pi**(-0.25)
+    output = np.sqrt(1/s) * wavelet
+    return output
+
+
+def cwt(data, wavelet, widths, dtype=None, **kwargs):
+    """
+    Continuous wavelet transform.
+
+    Performs a continuous wavelet transform on `data`,
+    using the `wavelet` function. A CWT performs a convolution
+    with `data` using the `wavelet` function, which is characterized
+    by a width parameter and length parameter. The `wavelet` function
+    is allowed to be complex.
+
+    Parameters
+    ----------
+    data : (N,) ndarray
+        data on which to perform the transform.
+    wavelet : function
+        Wavelet function, which should take 2 arguments.
+        The first argument is the number of points that the returned vector
+        will have (len(wavelet(length,width)) == length).
+        The second is a width parameter, defining the size of the wavelet
+        (e.g. standard deviation of a gaussian). See `ricker`, which
+        satisfies these requirements.
+    widths : (M,) sequence
+        Widths to use for transform.
+    dtype : data-type, optional
+        The desired data type of output. Defaults to ``float64`` if the
+        output of `wavelet` is real and ``complex128`` if it is complex.
+
+        .. versionadded:: 1.4.0
+
+    kwargs
+        Keyword arguments passed to wavelet function.
+
+        .. versionadded:: 1.4.0
+
+    Returns
+    -------
+    cwt: (M, N) ndarray
+        Will have shape of (len(widths), len(data)).
+
+    Notes
+    -----
+
+    .. versionadded:: 1.4.0
+
+    For non-symmetric, complex-valued wavelets, the input signal is convolved
+    with the time-reversed complex-conjugate of the wavelet data [1].
+
+    ::
+
+        length = min(10 * width[ii], len(data))
+        cwt[ii,:] = signal.convolve(data, np.conj(wavelet(length, width[ii],
+                                        **kwargs))[::-1], mode='same')
+
+    References
+    ----------
+    .. [1] S. Mallat, "A Wavelet Tour of Signal Processing (3rd Edition)",
+        Academic Press, 2009.
+
+    Examples
+    --------
+    >>> from scipy import signal
+    >>> import matplotlib.pyplot as plt
+    >>> t = np.linspace(-1, 1, 200, endpoint=False)
+    >>> sig  = np.cos(2 * np.pi * 7 * t) + signal.gausspulse(t - 0.4, fc=2)
+    >>> widths = np.arange(1, 31)
+    >>> cwtmatr = signal.cwt(sig, signal.ricker, widths)
+    >>> plt.imshow(cwtmatr, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto',
+    ...            vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max())
+    >>> plt.show()
+    """
+    if wavelet == ricker:
+        window_size = kwargs.pop('window_size', None)
+    # Determine output type
+    if dtype is None:
+        if np.asarray(wavelet(1, widths[0], **kwargs)).dtype.char in 'FDG':
+            dtype = np.complex128
+        else:
+            dtype = np.float64
+
+    output = np.zeros((len(widths), len(data)), dtype=dtype)
+    for ind, width in enumerate(widths):
+        N = np.min([10 * width, len(data)])
+        # the conditional block below and the window_size
+        # kwarg pop above may be removed eventually; these
+        # are shims for 32-bit arch + NumPy <= 1.14.5 to
+        # address gh-11095
+        if wavelet == ricker and window_size is None:
+            ceil = np.ceil(N)
+            if ceil != N:
+                N = int(N)
+        wavelet_data = np.conj(wavelet(N, width, **kwargs)[::-1])
+        output[ind] = convolve(data, wavelet_data, mode='same')
+    return output

venv/Lib/site-packages/scipy/signal/windows/__init__.py

@@ -0,0 +1,47 @@
+"""
+Window functions (:mod:`scipy.signal.windows`)
+==============================================
+
+The suite of window functions for filtering and spectral estimation.
+
+.. currentmodule:: scipy.signal.windows
+
+.. autosummary::
+   :toctree: generated/
+
+   get_window        -- Return a window of a given length and type.
+
+   barthann          -- Bartlett-Hann window
+   bartlett          -- Bartlett window
+   blackman          -- Blackman window
+   blackmanharris    -- Minimum 4-term Blackman-Harris window
+   bohman            -- Bohman window
+   boxcar            -- Boxcar window
+   chebwin           -- Dolph-Chebyshev window
+   cosine            -- Cosine window
+   dpss              -- Discrete prolate spheroidal sequences
+   exponential       -- Exponential window
+   flattop           -- Flat top window
+   gaussian          -- Gaussian window
+   general_cosine    -- Generalized Cosine window
+   general_gaussian  -- Generalized Gaussian window
+   general_hamming   -- Generalized Hamming window
+   hamming           -- Hamming window
+   hann              -- Hann window
+   hanning           -- Hann window
+   kaiser            -- Kaiser window
+   nuttall           -- Nuttall's minimum 4-term Blackman-Harris window
+   parzen            -- Parzen window
+   slepian           -- Slepian window
+   triang            -- Triangular window
+   tukey             -- Tukey window
+
+"""
+
+from .windows import *
+
+__all__ = ['boxcar', 'triang', 'parzen', 'bohman', 'blackman', 'nuttall',
+           'blackmanharris', 'flattop', 'bartlett', 'hanning', 'barthann',
+           'hamming', 'kaiser', 'gaussian', 'general_gaussian', 'general_cosine',
+           'general_hamming', 'chebwin', 'slepian', 'cosine', 'hann',
+           'exponential', 'tukey', 'get_window', 'dpss']

venv/Lib/site-packages/scipy/signal/windows/setup.py

@@ -0,0 +1,9 @@
+
+def configuration(parent_package='', top_path=None):
+    from numpy.distutils.misc_util import Configuration
+
+    config = Configuration('windows', parent_package, top_path)
+
+    config.add_data_dir('tests')
+
+    return config