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)

Parameters

waveletWavelet instance or str

Wavelet to integrate. If a string, should be the name of a wavelet.

scalescalar

precisionint, optional

Precision that will be used for wavelet function approximation computed with wavelet.wavefun(level=precision). Default is 8.

Returns

freqscalar

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 avialable 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 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')