Title :
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
Abstract :
In this paper, the notion of matrix-valued multiresolution analysis of space L2(Rs,Cr×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(Rs,Cr×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(Rs,CrÃ\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;
Conference_Titel :
Power Electronics and Intelligent Transportation System (PEITS), 2009 2nd International Conference on
Conference_Location :
Shenzhen
Print_ISBN :
978-1-4244-4544-8
DOI :
10.1109/PEITS.2009.5406928
