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.
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.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第3期1-5,共5页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(10571113)
关键词
正交双向小波
双向多分辨分析
MALLAT算法
orthonormal two-direction wavelet
two-direction multi-resolution analysis
Mallat algorithm
