多元向量值正交小波包的刻画

数学季刊 ›› 2008, Vol. 23 ›› Issue (4): 606-614.

多元向量值正交小波包的刻画

School of Education,Nanyang Institute of Technology,Nanyang 473000,China

收稿日期:2007-04-23 出版日期:2008-12-30 发布日期:2023-09-18
作者简介: HUA De-lin(1963-), male, native of Nanyang, Henan, a lecturer of Nanyang Institute of Tech- nology, engages in wavelet theory and applications.
基金资助:
Supported by the Natural Science Foundation of China(10571113)；

Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets

School of Education,Nanyang Institute of Technology,Nanyang 473000,China

Received:2007-04-23 Online:2008-12-30 Published:2023-09-18
About author: HUA De-lin(1963-), male, native of Nanyang, Henan, a lecturer of Nanyang Institute of Tech- nology, engages in wavelet theory and applications.
Supported by:
Supported by the Natural Science Foundation of China(10571113)；

摘要/Abstract

摘要： In this paper,the notion of orthogonal vector-valued wavelet packets of space L²(R^s,Cⁿ) is introduced.A procedure for constructing the orthogonal vector-valued wavelet packets is presented.Their properties are characterized by virtue of time-frequency analysis method,matrix theory and finite group theory,and three orthogonality formulas are obtained.Finally,new orthonormal bases of space L²(R^s,Cⁿ) are extracted from these wavelet packets.

关键词: orthogonality, refinement equation, vector-valued multiresolution analysis, vector-valued scaling function, vector-valued wavelet packets

Abstract: In this paper,the notion of orthogonal vector-valued wavelet packets of space L²(R^s,Cⁿ) is introduced.A procedure for constructing the orthogonal vector-valued wavelet packets is presented.Their properties are characterized by virtue of time-frequency analysis method,matrix theory and finite group theory,and three orthogonality formulas are obtained.Finally,new orthonormal bases of space L²(R^s,Cⁿ) are extracted from these wavelet packets.

Key words: orthogonality, refinement equation, vector-valued multiresolution analysis, vector-valued scaling function, vector-valued wavelet packets

中图分类号:

O174.2

华德林, 冯金顺. 多元向量值正交小波包的刻画[J]. 数学季刊, 2008, 23(4): 606-614.

HUA De-lin, FENG Jin-shun. Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets [J]. Chinese Quarterly Journal of Mathematics, 2008, 23(4): 606-614.

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