A unified approach for constructing multi-wavelets

Abstract

A unified approach for constructing a large class of multi-wavelets is presented, This class includes Geranimo Hardin Massopust, Alpert and Daubechies-like multi-wavelets. The main emphasis is on approximation order of the resulting multi-scaling functions. The unified approach involves formulating the approximation order condition in the framework of super functions and recognizing that the generalized left eigenvectors of the resulting finite down-sampled convolution matrix gives the coefficients that enter the finite linear combination of scaling functions which produces the desired super function from which polynomials of desired degree can be locally approximated.