The Characterization of a Sort of Biorthogonal Multivariate Wavelet Packets According to an Integer-valued Dilation Matrix

Author

Ma, Jinshuan ; Tian, Xinxian

Author_Institution

Sch. of Educ., Nanyang Inst. of Technol., Nanyang, China

Volume

3

fYear

2009

fDate

21-22 Nov. 2009

Firstpage

636

Lastpage

639

Abstract

The notion of matrix-valued multiresolution analysis of space of matrix-valued multivariate functions is proposed. An approach for constructing orthogonal matrix-valued multivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal bases of L²(R^s, C^rÃ—r) are obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.

Keywords

functional analysis; matrix algebra; time-frequency analysis; wavelet transforms; biorthogonal multivariate wavelet packets; functional analysis method; integer valued dilation matrix; matrix theory; matrix valued multiresolution analysis; matrix valued wavelet packets; orthogonality formulas; orthonormal bases; time frequency analysis method; Discrete transforms; Educational technology; Functional analysis; Information technology; Multiresolution analysis; Space technology; Time frequency analysis; Variable speed drives; Wavelet analysis; Wavelet packets; biorthogonal; matrix theory; matrix-valued wavelet packets; multivariate; orthonormal bases;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Information Technology Application, 2009. IITA 2009. Third International Symposium on

Conference_Location

Nanchang

Print_ISBN

978-0-7695-3859-4

Type

conf

DOI

10.1109/IITA.2009.247

Filename

5370189