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在有限长信号的小波变换中，一般说来零延拓不是一种好的边界处理方法，但对有些类别的小波，零延拓却能带来处理上的很大方便和收到良好的效果．本文主要探讨了正交小波中低通滤波器ｈｎ的支撑为［０，Ｍ］（即ｈｎ≠０，ｎ＝０，１，…，Ｍ；ｈｎ＝０，ｎ为其它值）的小波变换的边界处理问题，提出了零延拓是其较好的选择．我们首先利用小波变换的性质证明了一个有意义的结论，然后由这个结论证明了这类小波边界零延拓的可完全恢复性，并给出了一种无失真恢复算法，最后把这种方法与其它几种边界处理方法作了比较，指出了这种边界处理的几个优点：一是边界的完全可恢复性；二是完全重构综合滤波器构造的简单性；三是滤波器的性能在边界处的稳定性．
In the finite-length signal wavelet transform, in general, zero-extension is not a good boundary treatment, but for some types of wavelet, zero-extension can bring great convenience and receive good results . This paper mainly discusses the wavelet transform of the low-pass filter hn in orthogonal wavelet [0, M] (ie hn ≠ 0, n = 0,1, ..., M; hn = 0, n is other values) Border treatment problems, put forward zero extension is its better choice. We first prove a meaningful conclusion by using the nature of wavelet transform, and then prove the complete recoverability of zero-extension of such wavelet boundary by this conclusion and give a distortion-free recovery algorithm. Finally, this method Compared with several other boundary processing methods, some advantages of this boundary processing are pointed out: one is the complete recoverability of the boundary; the other is the simplicity of the fully reconstructed synthesis filter structure; the other is the performance of the filter Stability at the border.