Representations of stochastic processes using coiflet-type wavelets

The wavelet series expansion requires a high computational complexity; by means of projection, the scaling coefficients are computed at the finest scale in order to realize the Mallat algorithm to compute the wavelet coefficients at coarser scales. We propose a fast and practical algorithm to approximate the wavelet series expansion. The algorithm is based on sampling and reconstruction with coiflet-type wavelets, which possess vanishing moments on both scaling function and wavelet. We evaluate the performance of the algorithm by establishing the convergence rates and asymptotic forms for the mean-square errors in the scaling coefficients and wavelet coefficients of the synthesized stochastic process