杨守志,申培萍,杨建伟.矩阵的正交扩充与多正交小波[J].数学研究及应用,2003,23(3):525~534 |
矩阵的正交扩充与多正交小波 |
Matrix Orthogonal Extension and Orthogonal Multiwavelets with Scale=a |
投稿时间:2000-11-24 |
DOI:10.3770/j.issn:1000-341X.2003.03.025 |
中文关键词: 紧支撑函数 多尺度函数 正交多小波 两尺度矩阵方程 两尺度矩阵符号 两尺度矩阵序列 |
英文关键词:compactly supported function multiscaling function Orthogonal multiwavelets two-scale matrix equation two-scale matrix sequence two-scale matrix symbol. |
基金项目:河南省自然科学基金(984051900)和河南省教委自然科学基金(98110015)资助项目. |
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中文摘要: |
给出一种由a尺度紧支撑正交多尺度函数构造短支撑正交多小波的方法,其过程仅仅应用矩阵的正交扩充和求解方程组。如果r重尺度函数的支撑区间较大,可以将其转化为ar重短支撑情形,从而使得本文的方法适用于任意紧支撑正交多小波的构造,文后给出多小波的构造算例。 |
英文摘要: |
There are perfect formulas for the constructions of orthogonal uni-wavelet with scale = 2. However, as yet there has not been a general method to obtain orthogonal multi-wavelets with scale = a (a∈Z, a≥2 ). In this paper, we will give an approach for constructing compactly supported orthogonal multiwavelets with scale = a, which makes construction of orthogonal multiwavelets easy like in the construction of orthogonal uni-wavelet. Finally, an example for construction multiwavelets is given. |
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