/usr/lib/python2.7/dist-packages/pywt/_functions.py is in python-pywt 0.5.1-1.1ubuntu4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 | # Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
# Copyright (c) 2012-2016 The PyWavelets Developers
# <https://github.com/PyWavelets/pywt>
# See COPYING for license details.
"""
Other wavelet related functions.
"""
from __future__ import division, print_function, absolute_import
import warnings
import numpy as np
from numpy.fft import fft
from ._extensions._pywt import DiscreteContinuousWavelet, Wavelet, ContinuousWavelet
__all__ = ["integrate_wavelet", "central_frequency", "scale2frequency", "qmf",
"orthogonal_filter_bank",
"intwave", "centrfrq", "scal2frq", "orthfilt"]
_DEPRECATION_MSG = ("`{old}` has been renamed to `{new}` and will "
"be removed in a future version of pywt.")
def _integrate(arr, step):
integral = np.cumsum(arr)
integral *= step
return integral
def intwave(*args, **kwargs):
msg = _DEPRECATION_MSG.format(old='intwave', new='integrate_wavelet')
warnings.warn(msg, DeprecationWarning)
return integrate_wavelet(*args, **kwargs)
def centrfrq(*args, **kwargs):
msg = _DEPRECATION_MSG.format(old='centrfrq', new='central_frequency')
warnings.warn(msg, DeprecationWarning)
return central_frequency(*args, **kwargs)
def scal2frq(*args, **kwargs):
msg = _DEPRECATION_MSG.format(old='scal2frq', new='scale2frequency')
warnings.warn(msg, DeprecationWarning)
return scale2frequency(*args, **kwargs)
def orthfilt(*args, **kwargs):
msg = _DEPRECATION_MSG.format(old='orthfilt', new='orthogonal_filter_bank')
warnings.warn(msg, DeprecationWarning)
return orthogonal_filter_bank(*args, **kwargs)
def integrate_wavelet(wavelet, precision=8):
"""
Integrate `psi` wavelet function from -Inf to x using the rectangle
integration method.
Parameters
----------
wavelet : Wavelet instance or str
Wavelet to integrate. If a string, should be the name of a wavelet.
precision : int, optional
Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet's method (default: 8).
Returns
-------
[int_psi, x] :
for orthogonal wavelets
[int_psi_d, int_psi_r, x] :
for other wavelets
Examples
--------
>>> from pywt import Wavelet, integrate_wavelet
>>> wavelet1 = Wavelet('db2')
>>> [int_psi, x] = integrate_wavelet(wavelet1, precision=5)
>>> wavelet2 = Wavelet('bior1.3')
>>> [int_psi_d, int_psi_r, x] = integrate_wavelet(wavelet2, precision=5)
"""
# FIXME: this function should really use scipy.integrate.quad
if type(wavelet) in (tuple, list):
msg = ("Integration of a general signal is deprecated "
"and will be removed in a future version of pywt.")
warnings.warn(msg, DeprecationWarning)
elif not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
wavelet = DiscreteContinuousWavelet(wavelet)
if type(wavelet) in (tuple, list):
psi, x = np.asarray(wavelet[0]), np.asarray(wavelet[1])
step = x[1] - x[0]
return _integrate(psi, step), x
functions_approximations = wavelet.wavefun(precision)
if len(functions_approximations) == 2: # continuous wavelet
psi, x = functions_approximations
step = x[1] - x[0]
return _integrate(psi, step), x
elif len(functions_approximations) == 3: # orthogonal wavelet
phi, psi, x = functions_approximations
step = x[1] - x[0]
return _integrate(psi, step), x
else: # biorthogonal wavelet
phi_d, psi_d, phi_r, psi_r, x = functions_approximations
step = x[1] - x[0]
return _integrate(psi_d, step), _integrate(psi_r, step), x
def central_frequency(wavelet, precision=8):
"""
Computes the central frequency of the `psi` wavelet function.
Parameters
----------
wavelet : Wavelet instance, str or tuple
Wavelet to integrate. If a string, should be the name of a wavelet.
precision : int, optional
Precision that will be used for wavelet function
approximation computed with the wavefun(level=precision)
Wavelet's method (default: 8).
Returns
-------
scalar
"""
if not isinstance(wavelet, (Wavelet, ContinuousWavelet)):
wavelet = DiscreteContinuousWavelet(wavelet)
functions_approximations = wavelet.wavefun(precision)
if len(functions_approximations) == 2:
psi, x = functions_approximations
else:
# (psi, x) for (phi, psi, x)
# (psi_d, x) for (phi_d, psi_d, phi_r, psi_r, x)
psi, x = functions_approximations[1], functions_approximations[-1]
domain = float(x[-1] - x[0])
assert domain > 0
index = np.argmax(abs(fft(psi)[1:])) + 2
if index > len(psi) / 2:
index = len(psi) - index + 2
return 1.0 / (domain / (index - 1))
def scale2frequency(wavelet, scale, precision=8):
"""
Parameters
----------
wavelet : Wavelet instance or str
Wavelet to integrate. If a string, should be the name of a wavelet.
scale : scalar
precision : int, optional
Precision that will be used for wavelet function approximation computed
with ``wavelet.wavefun(level=precision)``. Default is 8.
Returns
-------
freq : scalar
"""
return central_frequency(wavelet, precision=precision) / scale
def qmf(filt):
"""
Returns the Quadrature Mirror Filter(QMF).
The magnitude response of QMF is mirror image about `pi/2` of that of the
input filter.
Parameters
----------
filt : array_like
Input filter for which QMF needs to be computed.
Returns
-------
qm_filter : ndarray
Quadrature mirror of the input filter.
"""
qm_filter = np.array(filt)[::-1]
qm_filter[1::2] = -qm_filter[1::2]
return qm_filter
def orthogonal_filter_bank(scaling_filter):
"""
Returns the orthogonal filter bank.
The orthogonal filter bank consists of the HPFs and LPFs at
decomposition and reconstruction stage for the input scaling filter.
Parameters
----------
scaling_filter : array_like
Input scaling filter (father wavelet).
Returns
-------
orth_filt_bank : tuple of 4 ndarrays
The orthogonal filter bank of the input scaling filter in the order :
1] Decomposition LPF
2] Decomposition HPF
3] Reconstruction LPF
4] Reconstruction HPF
"""
if not (len(scaling_filter) % 2 == 0):
raise ValueError("`scaling_filter` length has to be even.")
scaling_filter = np.asarray(scaling_filter, dtype=np.float64)
rec_lo = np.sqrt(2) * scaling_filter / np.sum(scaling_filter)
dec_lo = rec_lo[::-1]
rec_hi = qmf(rec_lo)
dec_hi = rec_hi[::-1]
orth_filt_bank = (dec_lo, dec_hi, rec_lo, rec_hi)
return orth_filt_bank
|