# 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). [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: 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). 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. freq : scalar

pywt.qmf(filt)

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. 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). 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 case-insensitive). 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. 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] (1, 2) D.L. Donoho and I.M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, vol. 81, pp. 425–455, 1994.
 [2] (1, 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')
>>> available_signals = pywt.data.demo_signal('list')