向量值双正交小波的存在性及滤波器的构造  

On the existence and the construction of biorthogonal vector-valued wavelets

作　　者：陈清江[1] 陈瑛[2] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]漯河职业技术学院,河南漯河462002

出　　处：《纯粹数学与应用数学》2008年第1期10-16,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金(10571113);西安建筑科技大学人才基金与基础研究基金(RC0701;JC0718)

摘　　要：引进了向量值多分辨分析与向量值双正交小波的概念.讨论了向量值双正交小波的存在性.运用多分辨分析和矩阵理论,给出一类紧支撑向量值双正交小波滤波器的构造算法.最后,给出4-系数向量值双正交小波滤波器的的构造算例.The notion of vector-valued multiresolution analysis is introduced and the definition of biorthogonal vector-valued wavelets is given. The existence of biorthogonal compactly supported vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. An algorithm for constructing a class of biorthogonal compactly supported vector-valued wavelets is presented by virtue of multiresolution analysis and matrix theory. A constructive example of filter banks of biorthogonal compactly supported vector-valued wavelets is presented.

关 键 词：双正交 向量值多分辨分析 向量值尺度函数 向量值小波 加细方程 

分 类 号：O174.2[理学—数学]