Boundary extension is necessary in time-limited signal processing.By analyzing a Mallat algorithm,four kinds of boundary extension methods commonly used in Mallat algorithm of finite length signal are studied.The general process of the wavelet transform with four boundary extension methods is derived.Two symmetric extension methods are discussed.The implementation of the wavelet decomposition and the perfect reconstruction is studied,whatever the length of the signal or the length of the filter is odd or even.In addition,in order to achieve multi-level decomposition and reconstruction,binary indicator series is adopted in periodic extension and symmetric extension.And this makes the wavelet transform easily implemented by programming.An example using bior4.4 bi-orthogonal wavelet is given to show that the proposed method preserves the perfect reconstruction while keeping the signal length unchanged.%处理有限长度信号时需要对其边界做某种延拓处理.本文在对Mallat算法分析的基础上,研究了有限长度信号Mallat算法中常用的4种边界延拓方法,并详细推导了4种边界延拓方法实现小波变换的一般过程.详细讨论了对称延拓中的2种延拓方式,分别就滤波器长度和信号长度为奇数或偶数的情况进行了研究.在周期延拓和对称延拓中,为了使多级分解与重构顺利进行,引入一个二元标示序列,使得小波变换便于编程实现.最后以bior4.4双正交小波给出实例,计算结果表明,在保持信号长度不变的情况下,按本文延拓方法能实现完全重构.
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