241 lines
6.8 KiB
Python
241 lines
6.8 KiB
Python
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
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# Copyright (c) 2012-2016 The PyWavelets Developers
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# <https://github.com/PyWavelets/pywt>
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# See COPYING for license details.
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"""
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Other wavelet related functions.
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"""
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from __future__ import division, print_function, absolute_import
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import warnings
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import numpy as np
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from numpy.fft import fft
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from ._extensions._pywt import DiscreteContinuousWavelet, Wavelet, ContinuousWavelet
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__all__ = ["integrate_wavelet", "central_frequency", "scale2frequency", "qmf",
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"orthogonal_filter_bank",
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"intwave", "centrfrq", "scal2frq", "orthfilt"]
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_DEPRECATION_MSG = ("`{old}` has been renamed to `{new}` and will "
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"be removed in a future version of pywt.")
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def _integrate(arr, step):
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integral = np.cumsum(arr)
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integral *= step
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return integral
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def intwave(*args, **kwargs):
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msg = _DEPRECATION_MSG.format(old='intwave', new='integrate_wavelet')
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warnings.warn(msg, DeprecationWarning)
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return integrate_wavelet(*args, **kwargs)
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def centrfrq(*args, **kwargs):
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msg = _DEPRECATION_MSG.format(old='centrfrq', new='central_frequency')
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warnings.warn(msg, DeprecationWarning)
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return central_frequency(*args, **kwargs)
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def scal2frq(*args, **kwargs):
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msg = _DEPRECATION_MSG.format(old='scal2frq', new='scale2frequency')
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warnings.warn(msg, DeprecationWarning)
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return scale2frequency(*args, **kwargs)
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def orthfilt(*args, **kwargs):
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msg = _DEPRECATION_MSG.format(old='orthfilt', new='orthogonal_filter_bank')
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warnings.warn(msg, DeprecationWarning)
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return orthogonal_filter_bank(*args, **kwargs)
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def integrate_wavelet(wavelet, precision=8):
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"""
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Integrate `psi` wavelet function from -Inf to x using the rectangle
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integration method.
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Parameters
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----------
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wavelet : Wavelet instance or str
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Wavelet to integrate. If a string, should be the name of a wavelet.
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precision : int, optional
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Precision that will be used for wavelet function
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approximation computed with the wavefun(level=precision)
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Wavelet's method (default: 8).
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Returns
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-------
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[int_psi, x] :
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for orthogonal wavelets
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[int_psi_d, int_psi_r, x] :
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for other wavelets
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Examples
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--------
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>>> from pywt import Wavelet, integrate_wavelet
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>>> wavelet1 = Wavelet('db2')
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>>> [int_psi, x] = integrate_wavelet(wavelet1, precision=5)
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>>> wavelet2 = Wavelet('bior1.3')
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>>> [int_psi_d, int_psi_r, x] = integrate_wavelet(wavelet2, precision=5)
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"""
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# FIXME: this function should really use scipy.integrate.quad
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if type(wavelet) in (tuple, list):
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msg = ("Integration of a general signal is deprecated "
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"and will be removed in a future version of pywt.")
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warnings.warn(msg, DeprecationWarning)
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elif not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
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wavelet = DiscreteContinuousWavelet(wavelet)
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if type(wavelet) in (tuple, list):
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psi, x = np.asarray(wavelet[0]), np.asarray(wavelet[1])
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step = x[1] - x[0]
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return _integrate(psi, step), x
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functions_approximations = wavelet.wavefun(precision)
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if len(functions_approximations) == 2: # continuous wavelet
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psi, x = functions_approximations
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step = x[1] - x[0]
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return _integrate(psi, step), x
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elif len(functions_approximations) == 3: # orthogonal wavelet
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phi, psi, x = functions_approximations
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step = x[1] - x[0]
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return _integrate(psi, step), x
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else: # biorthogonal wavelet
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phi_d, psi_d, phi_r, psi_r, x = functions_approximations
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step = x[1] - x[0]
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return _integrate(psi_d, step), _integrate(psi_r, step), x
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def central_frequency(wavelet, precision=8):
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"""
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Computes the central frequency of the `psi` wavelet function.
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Parameters
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----------
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wavelet : Wavelet instance, str or tuple
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Wavelet to integrate. If a string, should be the name of a wavelet.
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precision : int, optional
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Precision that will be used for wavelet function
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approximation computed with the wavefun(level=precision)
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Wavelet's method (default: 8).
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Returns
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-------
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scalar
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"""
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if not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
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wavelet = DiscreteContinuousWavelet(wavelet)
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functions_approximations = wavelet.wavefun(precision)
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if len(functions_approximations) == 2:
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psi, x = functions_approximations
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else:
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# (psi, x) for (phi, psi, x)
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# (psi_d, x) for (phi_d, psi_d, phi_r, psi_r, x)
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psi, x = functions_approximations[1], functions_approximations[-1]
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domain = float(x[-1] - x[0])
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assert domain > 0
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index = np.argmax(abs(fft(psi)[1:])) + 2
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if index > len(psi) / 2:
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index = len(psi) - index + 2
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return 1.0 / (domain / (index - 1))
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def scale2frequency(wavelet, scale, precision=8):
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"""
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Parameters
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----------
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wavelet : Wavelet instance or str
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Wavelet to integrate. If a string, should be the name of a wavelet.
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scale : scalar
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precision : int, optional
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Precision that will be used for wavelet function approximation computed
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with ``wavelet.wavefun(level=precision)``. Default is 8.
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Returns
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-------
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freq : scalar
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"""
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return central_frequency(wavelet, precision=precision) / scale
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def qmf(filt):
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"""
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Returns the Quadrature Mirror Filter(QMF).
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The magnitude response of QMF is mirror image about `pi/2` of that of the
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input filter.
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Parameters
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----------
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filt : array_like
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Input filter for which QMF needs to be computed.
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Returns
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-------
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qm_filter : ndarray
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Quadrature mirror of the input filter.
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"""
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qm_filter = np.array(filt)[::-1]
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qm_filter[1::2] = -qm_filter[1::2]
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return qm_filter
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def orthogonal_filter_bank(scaling_filter):
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"""
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Returns the orthogonal filter bank.
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The orthogonal filter bank consists of the HPFs and LPFs at
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decomposition and reconstruction stage for the input scaling filter.
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Parameters
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----------
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scaling_filter : array_like
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Input scaling filter (father wavelet).
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Returns
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-------
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orth_filt_bank : tuple of 4 ndarrays
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The orthogonal filter bank of the input scaling filter in the order :
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1] Decomposition LPF
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2] Decomposition HPF
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3] Reconstruction LPF
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4] Reconstruction HPF
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"""
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if not (len(scaling_filter) % 2 == 0):
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raise ValueError("`scaling_filter` length has to be even.")
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scaling_filter = np.asarray(scaling_filter, dtype=np.float64)
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rec_lo = np.sqrt(2) * scaling_filter / np.sum(scaling_filter)
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dec_lo = rec_lo[::-1]
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rec_hi = qmf(rec_lo)
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dec_hi = rec_hi[::-1]
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orth_filt_bank = (dec_lo, dec_hi, rec_lo, rec_hi)
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return orth_filt_bank
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