scipy.signal.cascade

scipy.signal.cascade(hk, J=7)

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

Inputs:

hk – coefficients of low-pass filter J – values will be computed at grid points $K/2^J$

Outputs:

x – the dyadic points $K/2^J$ for $K=0...N*(2^J)-1$

where len(hk)=len(gk)=N+1

phi – the scaling function phi(x) at x

$phi(x) = sum_{k=0}^{N} h_k phi(2x-k)$

psi – the wavelet function psi(x) at x

$psi(x) = sum_{k=0}^N g_k phi(2x-k)$

Only returned if gk is not None

Algorithm:

Uses the vector cascade algorithm described by Strang and Nguyen in “Wavelets and Filter Banks”

Builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at then end