### Navigation

- index
- modules |
- modules |
- next |
- previous |
- SciPy v0.9 Reference Guide (DRAFT) »
- Signal processing (`scipy.signal`) »

# scipy.signal.cascade

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

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

  Parameters : | hk : : Coefficients of low-pass filter. J : int. optional Values will be computed at grid points `K/2**J`.
  Returns : | 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: N phi(x) = sum hk * phi(2x-k) k=0 psi : : The wavelet function `psi(x)` at x: N phi(x) = sum gk * phi(2x-k) k=0 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.

### Navigation

- index
- modules |
- modules |
- next |
- previous |
- SciPy v0.9 Reference Guide (DRAFT) »
- Signal processing (`scipy.signal`) »