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
- waveletWavelet instance or str
Wavelet to integrate. If a string, should be the name of a wavelet.
- precisionint, 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 x-grid:
[int_psi, x_grid] = integrate_wavelet(wavelet, precision)
for other wavelets - integrals of decomposition and reconstruction wavelet functions and a corresponding x-grid:
[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
- waveletWavelet instance, str or tuple
Wavelet to integrate. If a string, should be the name of a wavelet.
- precisionint, 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)#
Convert from CWT “scale” to normalized frequency.
- Parameters
- waveletWavelet instance or str
Wavelet to integrate. If a string, should be the name of a wavelet.
- scalescalar
The scale of the CWT.
- precisionint, optional
Precision that will be used for wavelet function approximation computed with
wavelet.wavefun(level=precision). Default is 8.
- Returns
- freqscalar
Frequency normalized to the sampling frequency. In other words, for a sampling interval of dt seconds, the normalized frequency of 1.0 corresponds to (1/dt Hz).
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
- filtarray_like
Input filter for which QMF needs to be computed.
- Returns
- qm_filterndarray
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_filterarray_like
Input scaling filter (father wavelet).
- Returns
- orth_filt_banktuple 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 case-insensitive). If name is set to ‘list’, a list of the available test functions is returned.
- nint 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
- fnp.ndarray
Array of length
ncorresponding 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.
Examples
>>> import pywt >>> camera = pywt.data.camera() >>> doppler = pywt.data.demo_signal('doppler', 1024) >>> available_signals = pywt.data.demo_signal('list') >>> print(available_signals)