The characteristics of matrix-valued multidimensional wavelet packets with respect to an integer-valued dilation matrix

Author

Li, Qi ; Li, Hua

Author_Institution

Sch. of Sci., Xi´´an Univ. of Arch. & Tech, Xi´´an, China

Volume

2

fYear

2009

fDate

19-20 Dec. 2009

Firstpage

176

Lastpage

179

Abstract

In this paper, the notion of matrix-valued multiresolution analysis of space L²(R^s,C^rÃ—r) is introduced. A method for constructing biorthogonal matrix-valued multidimensional wavelet packets is developed and their properties are discussed 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 space L²(R^s,C^rÃ—r) is obtained by constructing a series of subspaces of biorthogonal vector-valued wavelet packets.

Keywords

matrix algebra; signal processing; time-frequency analysis; vectors; wavelet transforms; L²(R^s,C^rÃ\x97r) space; biorthogonal matrix; dilation matrix; matrix theory; multidimensional wavelet packets; operator theory; time-frequency analysis; vector-valued wavelet packets; Artificial intelligence; Computer science; Discrete wavelet transforms; Educational institutions; Intelligent transportation systems; Multidimensional systems; Multiresolution analysis; Power electronics; Wavelet analysis; Wavelet packets; Biorthogonality; matrix-valued wavelet packets; multiresolution analysis; multivariate; refinable equation;

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.2009.5406928

Filename

5406928