a尺度正交双向小波的Mallat算法-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

a尺度正交双向小波的Mallat算法

李万社，郝伟，蒙少亭

(陕西师范大学数学与信息科学学院，陕西西安 710062)

李万社，男，教授，博士，主要从事智能信号处理和小波与分形理论的应用研究.E-mail: liwsh@snnu.edu.cn.

摘要:

研究了a尺度正交双向小波的Mallat算法.引入了正交双向加细函数及a尺度正交双向小波的概念, 在此基础上利用a尺度正交双向多分辨分析, 得到了正交双向小波的分解与重构的Mallat算法, 并给出其矩阵表示,推导了信号分解后完全重构的充要条件. 该算法对于能量有限的离散信号的分解与重构有一定的实用价值.

关键词：

正交双向小波; 双向多分辨分析; Mallat算法

收稿日期：

2009-12-07

中图分类号：

O177.6

文献标识码：

文章编号：

1672-4291(2010)03-0001-05

基金项目：

国家自然科学基金资助项目（10571113）.

Doi:

The Mallat algorithm of orthonormal two-direction wavelets with dilation factor a

LI Wan-she, HAO Wei, MENG Shao-ting

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The Mallat algorithm of orthonormal two-direction wavelets with dilation factor a is discussed. The concepts of orthonormal two-direction refinable function and orthonormal two-direction wavelets with dilation factor a are introduced. Using the theory of orthonormal two-direction multi-resolution analysis with dilation factor a, the decomposition and reconstruction Mallat algorithm of orthonormal two-direction wavelets are obtained. the corresponding matrix representations are given. A necessary and sufficient condition of complete reconstruction with decomposition is deduced. This algorithm is important for the decomposition and reconstruction of discrete signal with finite energy.

KeyWords:

orthonormal two-direction wavelet; two-direction multi-resolution analysis; Mallat algorithm