# 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. ) as well as the wavelet book by Stéphane Mallat .

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

  D.L. Donoho and I.M. Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, vol. 81, pp. 425–455, 1994.
  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')