Constructions of Vector‐Valued Filters and Vector‐Valued Wavelets

Abstract

Leta =(a1,a2,…,am)∈ℂmbe anm-dimensional vector. Then, it can be identified with anm×mcirculant matrix. By using the theory of matrix-valued wavelet analysis (Walden and Serroukh, 2002), we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions are given. Specially, we deal with the construction of filters on symmetric matrix-valued functions space.