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.
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页码：1574 / 1587
页数：14
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