/usr/lib/python2.7/dist-packages/pywt/functions.py is in python-pywt 0.3.0-1build1.
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# Copyright (c) 2006-2012 Filip Wasilewski <http://en.ig.ma/>
# See COPYING for license details.
"""
Other wavelet related functions.
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.fft import fft
from ._pywt import Wavelet
__all__ = ["intwave", "centfrq", "scal2frq", "qmf", "orthfilt"]
WAVELET_CLASSES = (Wavelet)
def wavelet_for_name(name):
if not isinstance(name, str):
raise TypeError(
"Wavelet name must be of string type, not %s" % type(name))
try:
wavelet = Wavelet(name)
except ValueError:
raise ValueError("Invalid wavelet name - %s." % name)
return wavelet
def _integrate(arr, step):
integral = np.cumsum(arr)
integral *= step
return integral
def intwave(wavelet, precision=8):
"""
Integrate `psi` wavelet function from -Inf to x using the rectangle
integration method.
Parameters
----------
wavelet : Wavelet instance, str or tuple
Wavelet to integrate. If a string, should be the name of a wavelet.
If a tuple, should contain ``(wavelet function approx., x grid)``.
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
[int_function, x] :
for (function approx., x grid) pair
Notes
-----
(function_approx, x) :
Function to integrate on the x grid. Used instead
of Wavelet object to allow custom wavelet functions.
Examples
--------
>>> import pywt
>>> wavelet1 = pywt.Wavelet('db2')
>>> [int_psi, x] = pywt.intwave(wavelet1, precision=5)
>>> wavelet2 = pywt.Wavelet('bior1.3')
>>> [int_psi_d, int_psi_r, x] = pywt.intwave(wavelet2, precision=5)
"""
# FIXME: this function should really use scipy.integrate.quad
if isinstance(wavelet, tuple):
psi, x = np.asarray(wavelet[0]), np.asarray(wavelet[1])
step = x[1] - x[0]
return _integrate(psi, step), x
else:
if not isinstance(wavelet, WAVELET_CLASSES):
wavelet = wavelet_for_name(wavelet)
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 centfrq(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.
If a tuple, should contain ``(wavelet function approx., x grid)``.
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
Notes
-----
(function_approx, xgrid) :
Function defined on xgrid. Used instead
of Wavelet object to allow custom wavelet functions.
"""
# FIXME: `wavelet` handling should be identical to intwave, factor out
if isinstance(wavelet, tuple):
psi, x = np.asarray(wavelet[0]), np.asarray(wavelet[1])
else:
if not isinstance(wavelet, WAVELET_CLASSES):
wavelet = wavelet_for_name(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 scal2frq(wavelet, scale, delta, precision=8):
"""
Parameters
----------
wavelet : Wavelet instance, str or tuple
Wavelet to integrate. If a string, should be the name of a wavelet.
If a tuple, should contain ``(wavelet function approx., x grid)``.
scale : scalar
delta : scalar
sampling
precision : int, optional
Precision that will be used for wavelet function approximation computed
with ``wavelet.wavefun(level=precision)``. Default is 8.
Returns
-------
freq : scalar
Notes
-----
(function_approx, xgrid) :
Function defined on xgrid. Used instead
of Wavelet object to allow custom wavelet functions.
"""
return centfrq(wavelet, precision=precision) / (scale * delta)
def qmf(filter):
"""
Returns the Quadrature Mirror Filter(QMF).
The magnitude response of QMF is mirror image about `pi/2` of that of the
input filter.
Parameters
----------
filter : 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(filter)[::-1]
qm_filter[1::2] = -qm_filter[1::2]
return qm_filter
def orthfilt(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
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