The Research of a Two-directional Vector-valued Quarternary Wavelet Packets and Applications in Material Engineering

被引：0

作者：

Zhou, Jianfeng ^{[1
]}

机构：

[1] Xian Univ Arts & Sci, Sch Math & Comp, Xian 710065, Peoples R China

来源：

ADVANCES IN MANUFACTURING SCIENCE AND ENGINEERING, PTS 1-4 | 2013年 / 712-715卷

关键词：

Wavelet analysis; Vector scaling function; four-dimensional; vector-valued wavelet packets; frame packets; vector subdivision scheme; biorthogonality formulas;

D O I：

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

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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 definition 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 L-2 (R-4)(n) from these wavelet packets. The sufficient condition for the existence of four-dimensional wavelet packets is established based on the multiresolution analysis method.

引用

页码：2487 / 2492

页数：6

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