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中文摘要：
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.
英文摘要：
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.
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