dyadic.refine(f, x, j, fast=T) phi.at.integers(wp)
phi.at.integers
or the
function itself. Assumed to be sampled wavelet at every
2^-(j-1)
point,
the length should be
n=(m-1)*2^(j-1)+1
.
x
is assumed to be sampled at every
2^-(j-1)
point.
wavelet.packet
.
2*n-1=(m-1)*2^j+1
, sampled wavelet at every
2^-j
point.
The function
phi.at.integers
evaluates the values of the scaling function
at integers,
dyadic.refine
then computes the values of wavelet packet
function at dyadics using dilation equations.
Strang, G. (1989). Wavelets and Dilation Equations: A Brief Introduction. SIAM Review, Vol 31, pp.614-627.