矩阵的扩充与紧支撑多小波

journal6 ›› 2001, Vol. 22 ›› Issue (2): 44-49.

矩阵的扩充与紧支撑多小波

( 1.西安交通大学理学院科学计算与应用软件系, 陕西西安 710049; 2.郑州工程学院数理部, 河南郑州 450052)

出版日期:2001-06-15 发布日期:2013-01-05
作者简介:崔丽鸿( 1965- ) ,女, 副教授,西安交通大学理学院科学计算与应用软件系博士研究生,主要从事小波分析研究.

Matrix Extension and Compactly Supported Multi- wavelet

( 1. Dept. of Math. , Xi'an Jiaotong University, Xi'an 710049, China; 2. Zhengzhou Ins titute of Technology, Zhenzhou 450052, China)

Online:2001-06-15 Published:2013-01-05

摘要/Abstract

摘要：一个元素定义在复数域上的罗朗多项式的 n @ r 的矩阵 P( z)能被扩充为一个仿酉矩阵, 当 n= 2 时, 矩阵的扩充是唯一的;当 n≥3时,矩阵的扩充有无穷多种. 因此可用此方法构造出很多种不同的 r 重紧支撑向量小波和预小波( n≥3) , 从而也给出了同一尺度函数相对应的紧支撑向量小波或预小波非唯一的构造算法. 相应的小构造算例也说明了这一结果.

关键词： 小波基, 预小波, 矩阵的扩充, 仿酉矩阵, 多项式相位矩阵

Abstract: An n @ r mat rix P ( z ) , n [ r, wi th Laurent polynomial entries in one comple x variable z, can be e xtended to a paraunitary mat rix, and when n≥3 parauni tary extendingisn. t unique.The algori thm can be applied to the const ruction of compactly supported wavelets and pre wavelets from multi resolutions generated by serveral univariate scaling functions with an arbi trary di lation parpmeter. Finally, the corresponding examples are given.
Key words :

Key words: wavelet bases, prewavelets, matrix extension, paraunitray matrix, polyphase matrix

崔丽鸿, 阎运生. 矩阵的扩充与紧支撑多小波[J]. journal6, 2001, 22(2): 44-49.

CUI Li-Hong, YAN Yun-Sheng. Matrix Extension and Compactly Supported Multi- wavelet[J]. journal6, 2001, 22(2): 44-49.