Other functions¶
Integrating wavelet functions¶

pywt.
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)
The result of the call depends on the wavelet
argument:
for orthogonal and continuous wavelets  an integral of the wavelet function specified on an xgrid:
[int_psi, x_grid] = integrate_wavelet(wavelet, precision)
for other wavelets  integrals of decomposition and reconstruction wavelet functions and a corresponding xgrid:
[int_psi_d, int_psi_r, x_grid] = integrate_wavelet(wavelet, precision)
Central frequency of psi
wavelet function¶

pywt.
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

pywt.
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
Quadrature Mirror Filter¶

pywt.
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.
Orthogonal Filter Banks¶

pywt.
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
Example Datasets¶
The following example datasets are available in the module pywt.data
:
name description ecg ECG waveform (1024 samples) aero grayscale image (512x512) ascent grayscale image (512x512) camera grayscale image (512x512) nino sea surface temperature (264 samples) demo_signal various synthetic 1d test signals
Each can be loaded via a function of the same name.

pywt.data.
demo_signal
(name='Bumps', n=None)¶ Simple 1D wavelet test functions.
This function can generate a number of common 1D test signals used in papers by David Donoho and colleagues (e.g. [1]) as well as the wavelet book by Stéphane Mallat [2].
Parameters:  name : {‘Blocks’, ‘Bumps’, ‘HeaviSine’, ‘Doppler’, …}
The type of test signal to generate (name is caseinsensitive). If name is set to ‘list’, a list of the avialable test functions is returned.
 n : int or None
The length of the test signal. This should be provided for all test signals except ‘Gabor’ and ‘sineoneoverx’ which have a fixed length.
Returns:  f : np.ndarray
Array of length
n
corresponding to the specified test signal type.
Notes
This function is a partial reimplementation of the MakeSignal function from the [Wavelab](https://statweb.stanford.edu/~wavelab/) toolbox. These test signals are provided with permission of Dr. Donoho to encourage reproducible research.
References
[1] D.L. Donoho and I.M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, vol. 81, pp. 425–455, 1994. [2] S. Mallat. A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press. 2009.
Example:
>>> import pywt
>>> camera = pywt.data.camera()
>>> doppler = pywt.data.demo_signal('doppler', 1024)
>>> available_signals = pywt.data.demo_signal('list')