scipy.signal.cascade#
- scipy.signal.cascade(hk, J=7)[source]#
Return (x, phi, psi) at dyadic points
K/2**J
from filter coefficients.- Parameters
- hkarray_like
Coefficients of low-pass filter.
- Jint, optional
Values will be computed at grid points
K/2**J
. Default is 7.
- Returns
- xndarray
The dyadic points
K/2**J
forK=0...N * (2**J)-1
wherelen(hk) = len(gk) = N+1
.- phindarray
The scaling function
phi(x)
at x:phi(x) = sum(hk * phi(2x-k))
, where k is from 0 to N.- psindarray, 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.