scipy.signal.cascade¶

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 lowpass 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
forK=0...N * (2**J)1
wherelen(hk) = len(gk) = N+1
.phi : ndarray
The scaling function
phi(x)
at x:phi(x) = sum(hk * phi(2xk))
, where k is from 0 to N.psi : ndarray, optional
The wavelet function
psi(x)
at x:phi(x) = sum(gk * phi(2xk))
, 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.