A study of biorthogonal multiple vector-valued wavelets

被引：2

作者：

Han, Jincang ^{[1
,2
]}

Cheng, Zhengxing ^{[1
]}

Chen, Qingjiang ^{[3
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Sci, Xian 710049, Peoples R China

[2] Lanzhou Commercial Coll, Sch Informat, Lanzhou 730000, Peoples R China

[3] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2009年 / 40卷 / 04期

关键词：

SPACE-TIME; CONSTRUCTION; SIGNAL;

D O I：

10.1016/j.chaos.2007.09.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of vector-valued multiresolution analysis is introduced and the concept of biorthogonal multiple vector-valued wavelets which are wavelets for vector fields, is introduced. It is proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets is presented. Their properties are investigated by means of operator theory and algebra theory and time-frequency analysis method. Several biorthogonality formulas regarding these wavelet packets are obtained. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1574 / 1587

页数：14

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