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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
(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.
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)
Each can be loaded via a function of the same name.
Example: .. sourcecode:: python
>>> import pywt
>>> camera = pywt.data.camera()