Wavelet packet transform initialization for piecewise polynomial and bandlimited inputs

This paper considers the problem of initializing the wavelet packet transform when the analog input x(t) is either bandlimited or else is piecewise polynomial on the dyadic intervals. This is accomplished by the construction of certain prefilter sequences that are applied to the samples {x_k|x_k=x(kT)} (T is the sampling period). In the piecewise polynomial case, the prefilter sequences are computed with the aid of the interpolatory graphical display algorithm (IGDA), which is used to compute the so-called incremental moment functions of the scaling function φ(t) on the dyadic points. The moments of φ(t) are also employed