vector to be refined, should be an output of 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.
j:
sampling level, x is assumed to be sampled at every 2^-(j-1) point.
fast:
logical flag indicating if fast program should be used.
wp:
an object of wavelet.packet.
VALUE:
a refined vector of length 2*n-1=(m-1)*2^j+1, sampled wavelet at every
2^-j point.
DETAILS:
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.
REFERENCES:
Strang, G. (1989). Wavelets and Dilation Equations: A Brief Introduction.
SIAM Review, Vol 31, pp.614-627.