- scipy.signal.cascade(hk, J=7)¶
Return (x, phi, psi) at dyadic points K/2**J from filter coefficients.
hk : array_like
Coefficients of low-pass filter.
J : int, optional
Values will be computed at grid points K/2**J. Default is 7.
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.