scipy.signal.cascade(hk, J=7)[source]

Return (x, phi, psi) at dyadic points K/2**J from filter coefficients.

Parameters :

hk : array_like

Coefficients of low-pass filter.

J : int, optional

Values will be computed at grid points K/2**J. Default is 7.

Returns :

x : ndarray

The dyadic points K/2**J for K=0...N * (2**J)-1 where len(hk) = len(gk) = N+1.

phi : ndarray

The scaling function phi(x) at x: phi(x) = sum(hk * phi(2x-k)), where k is from 0 to N.

psi : ndarray, optional

The wavelet function psi(x) at x: phi(x) = sum(gk * phi(2x-k)), where k is from 0 to N. psi is only returned if gk is not None.


The algorithm uses the vector cascade algorithm described by Strang and Nguyen in “Wavelets and Filter Banks”. It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end.

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