Return (x, phi, psi) at dyadic points
K/2**Jfrom 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=0...N * (2**J)-1where
len(hk) = len(gk) = N+1.
- phi : ndarray
The scaling function
phi(x) = sum(hk * phi(2x-k)), where k is from 0 to N.
- psi : ndarray, optional
The wavelet function
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.