一类向量值正交小波的设计与性质  

Designment and Characters of a Sort of Orthogonal Vector-Valued Poly-Scaled Wavelets

作　　者：于育民[1] 吕保献[2] 程正兴[3] 

机构地区：[1]南阳理工学院应用数学系,河南南阳473004 [2]河南工业职业技术学院基础课教学部,河南南阳473009 [3]西安交通大学理学院,陕西西安710049

出　　处：《数学的实践与认识》2011年第8期217-227,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10571113)

摘　　要：引入整数因子伸缩的向量值正交小波与向量值小波包的概念.运用仿酉向量滤波器理论和矩阵理论,给出具有整数因子伸缩的向量值正交小波存在的充要条件.提供了紧支撑向量值正交的构建算法,给出了相应的构建算例.利用时频分析方法与算子理论,刻画了一类向量值正交小波包的性质,得到了整数伸缩的向量值小波包的正交公式.The notion of orthogonal vector-valued wavelets with poly-scale is introduced. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets with poly-scale is derived by vietue of paraunitary vector filter ban k theory and matrix theory. One constructive examples on vector-valued wavelets are presented. The concept of orthogonal multi-scaled vector-valued wavelet packets is introduced. Their properties are characterized, and two rthogonality formulas concerning the wavelet packets are established by using time- frequency analysis method and operator theory.

关 键 词：向量值小波 向量值尺度函数 时频分析方法 迭代算法 向量值小波包 小波包基 

分 类 号：O174.2[理学—数学]