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# The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets

## Abstract:

Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen- -sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

## Info:

Periodical:

Main Theme:

Edited by:

Yanwen Wu

Pages:

896-901

DOI:

10.4028/www.scientific.net/KEM.439-440.896

Citation:

Q. J. Chen and Y. Y. Wang, "The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets", Key Engineering Materials, Vols. 439-440, pp. 896-901, 2010

Online since:

June 2010

Authors:

Price:

$35.00

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