向量值正交小波的构造与向量值小波包的特征

数学季刊 ›› 2008, Vol. 23 ›› Issue (3): 360-367.

向量值正交小波的构造与向量值小波包的特征

1. School of Science,Xi'an University of Architecture and Technology 2. Institute of Higher Vocational Education,Shangqiu Vocational and Technical College

收稿日期:2007-05-18 出版日期:2008-09-30 发布日期:2023-09-21
作者简介:CHEN Qing-jiang(1966- ), male, native of Xinyang, Henan, an associate professor of Xi’an University of Architecture and Technology. Ph.D., engages in wavelet theory and its applications.
基金资助:
Supported by the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)；Supported by the Items of Xi’an University of Architecture and Technology(RC0701； JC0718)；

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

1. School of Science,Xi'an University of Architecture and Technology 2. Institute of Higher Vocational Education,Shangqiu Vocational and Technical College

Received:2007-05-18 Online:2008-09-30 Published:2023-09-21
About author:CHEN Qing-jiang(1966- ), male, native of Xinyang, Henan, an associate professor of Xi’an University of Architecture and Technology. Ph.D., engages in wavelet theory and its applications.
Supported by:
Supported by the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)；Supported by the Items of Xi’an University of Architecture and Technology(RC0701； JC0718)；

摘要/Abstract

摘要： The notion of vector-valued multiresolution analysis is introduced and the con-cept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and suffcient condition on the existence of orthogonal vector-valued wavelets is given by means of parauni-tary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L²(R,Cⁿ) from these wavelet packets.

关键词: orthogonal, Hermitian matrix, vector-valued multiresolution analysis, vectorvalued scaling functions, vector-valued wavelets, vector-valued wavelet packets

Abstract: The notion of vector-valued multiresolution analysis is introduced and the con-cept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and suffcient condition on the existence of orthogonal vector-valued wavelets is given by means of parauni-tary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L²(R,Cⁿ) from these wavelet packets.

Key words: orthogonal, Hermitian matrix, vector-valued multiresolution analysis, vectorvalued scaling functions, vector-valued wavelets, vector-valued wavelet packets

中图分类号:

O174.2

陈清江, 刘洪运. 向量值正交小波的构造与向量值小波包的特征[J]. 数学季刊, 2008, 23(3): 360-367.

CHEN Qing-jiang, LIU Hong-yun. Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(3): 360-367.

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