具有整数伸缩因子的向量值正交小波的构建算法与性质  

Constructive algorithm and properties of orthogonal vector-valued wavelets with integer expansion factor

作　　者：于育民[1] 连冬艳[1] 程正兴[2] 

机构地区：[1]南阳理工学院应用数学系,河南南阳473004 [2]西安交通大学理工学院,陕西西安710049

出　　处：《兰州理工大学学报》2011年第4期155-160,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10671154);陕西省自然科学基金(2009JM1002)

摘　　要：引进多尺度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,给出多尺度向量值正交小波存在的充要条件.提供紧支撑向量值正交的构建算法,给出相应的构建算例.利用时频分析方法与算子理论,刻画一类向量值正交小波包的性质.得到向量值小波包的正交公式.构造向量值函数空间L2(R,Cn)的规范正交基.The notion of orthogonal vector-valued wavelets with multiple scale and vector-valued wavelet packets were introduced.A necessary and sufficient condition on the existence of such wavelets was derived by virtue of the paraunitary vector filter bank theory and matrix theory.A constructive algorithm was provided for the vector with short support.A corresponding constructive example was given.By using time-frequency analysis method and operator theory,the properties of a class of vector-valued orthogonal wavelet packets were characterized and the orthogonality formula was obtained for the wavelet packets.The orthonormal base of vector-valued function space L2（R,Cn） was constructed.

关 键 词：向量值尺度函数 向量值小波 时频分析方法 向量值小波包 规范正交基 

分 类 号：O174.2[理学—数学]