Multiwavelet transforms based on several scaling functions

An algebraic method for the design of discrete wavelet transforms based on several scaling functions is presented. Solving systems of partly nonlinear equations is necessary to compute the discrete coefficients. Wavelet transforms based on several scaling functions enable properties that are impossible in the single-wavelet case. Wavelet transforms based on several scaling functions can also be designed wavelet-like, what leads to a better approximation of the continuous bases. In this paper we show how to construct the discrete wavelet transforms based on several scaling functions with the algebraic design method and discuss the properties of the resulting wavelet bases.<>