中文摘要：

本文研究多尺度双向向量值正交小波的存在性、构造算法与性质.利用多分辨分析理论,时频分析方法与矩阵理论,给出紧支撑多尺度双向向量值正交小波的构造算法,得到多尺度双向向量值小波包的正交公式与向量值小波包基.推广了向量值正交小波的概念.

英文摘要：

In this paper, existence and construction as well as properties of orthogonal two-direction vector-valued wavelets with multi-scale are investigated. A construction algorithm for compactly supported orthogonal two-direction vector-valued wavelets is presented by virtue of the multi-resolution analysis and time-frequency method as well as matrix theory. The orthogonality formulas for two-direction vector-valued wavelet packets with multi-scale and vector-valued wavelet packet bases are obtained. The notion for vector-valued wavelets is generalized.