Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation

Xin Xian Tian; Ai Lian Huo

doi:10.4028/www.scientific.net/AMM.20-23.1053

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 20-23Construction and Characteristics of a Kind of...

Construction and Characteristics of a Kind of Four-Dimensional Vector Wavelet Packets with Four-Scale Dilation

Abstract:

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

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Periodical:

Applied Mechanics and Materials (Volumes 20-23)

Pages:

1053-1059

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.20-23.1053

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Online since:

January 2010

Authors:

Xin Xian Tian, Ai Lian Huo

Keywords:

Biorthogonality, Four-Dimensional, Riesz Base, Vector-Valued, Wavelet Packet (WP)

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