关于多重向量值正交小波的存在性

On the Existence of Orthogonal Multiple Vector-Valued Wavelets

引进多重向量值多分辨分析与m(3≤m∈Z)尺度多重向量值正交小波的概念.运用仿酉向量滤波器理论与矩阵理论,得到多重向量值正交小波存在的充要条件.在给定滤波器的条件下,表明多重向量值正交尺度函数和正交小波函数可以由加细方程的解得到.

In this paper, multiple vector-valued multiresolution analysis and orthogonalmultiple vector-valued wavelets with scale m are introduced. A necessaryand suficient condition on the existence of orthogonal multiple vector-valued waveletsis derived by using paraunitary vector filter bank theory and matrix theory. It is shownhow to obtain orthogonal vector-valued scaling functions and wavelets from solving ref-inement equations if some filter banks are given.