The characterization of a sort of biorthogonal multivariate matrix wavelet packets according to a dilation matrix

Author

Lu, Jun ; Lv, Baoxian

Author_Institution

Dept. of Math., Zhengzhou Teachers´´ Coll., Zhengzhou, China

Volume

2

fYear

2009

fDate

19-20 Dec. 2009

Firstpage

196

Lastpage

199

Abstract

In this paper, the notion of matrix-valued multiresolution analysis is introduced. A method for constructing biorthogonal matrix-valued wavelet packets in higher dimensions is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of three dimensional matrix-valued function space are obtained by designing a series of subspaces of biorthogonal matrix wavelet packets.

Keywords

matrix algebra; signal processing; time-frequency analysis; wavelet transforms; Riesz basis; biorthogonal multivariate matrix wavelet packets; dilation matrix; matrix theory; operator theory; three dimensional matrix-valued function; time-frequency analysis method; Artificial intelligence; Discrete wavelet transforms; Educational institutions; Intelligent transportation systems; Mathematics; Multiresolution analysis; Power electronics; Time frequency analysis; Wavelet analysis; Wavelet packets; Biorthogonal; matrix-valued; multiresolution analysis; multivariate; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Power Electronics and Intelligent Transportation System (PEITS), 2009 2nd International Conference on

Conference_Location

Shenzhen

Print_ISBN

978-1-4244-4544-8

Type

conf

DOI

10.1109/PEITS.2009.5406921

Filename

5406921