scipy.signal.cascade¶

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

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

Parameters:

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 (2J)-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.

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.

Notes

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.