The Research of a Two-Directional Vector-Valued Quarternary Wavelet Packets and Applications in Material Engineering

Jian Feng Zhou

doi:10.4028/www.scientific.net/AMR.712-715.2487

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 712-715The Research of a Two-Directional Vector-Valued...

The Research of a Two-Directional Vector-Valued Quarternary Wavelet Packets and Applications in Material Engineering

Abstract:

In this paper, we introduce a class of vector-valued four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets. The defini -tion of biorthogonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method. Three biorthogonality formulas regarding the wavelet packets are established. Finally, it is shown how to draw new Riesz bases of space from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

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Periodical:

Advanced Materials Research (Volumes 712-715)

Pages:

2487-2492

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.712-715.2487

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Online since:

June 2013

Authors:

Jian Feng Zhou

Keywords:

Biorthogonality Formulas, Four-Dimensional, Frame Packets, Vector Scaling Function, Vector Subdivision Scheme, Vector-Valued Wavelet Pac-Kets, Wavelet Analysis

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