M-band multi-wavelets from spline super functions with approximation order

Abstract

A simple method for constructing M-band multi-wavelets using the super function idea is presented. The method is based on formulating the approximation order requirement in terms of a matrix equation and recognizing the generalized left eigenvectors of the matrix Lf a finite portion of the down sampled convolution matrix L as the coefficients that linearly combine to form the desired M-band spline super function with the desired approximation order. Several 3-band multi-wavelets with approximation orders two and three with multiplicity two and three are constructed.