在子带图象编码系统中，有限长度信号序列（如图象信号），存在由线性卷积引起的边界扩展效应。传统方法一般用圆卷积和对称扩展方法来减弱边界扩展效应，但实验结果表明边界还存在失真。为此，按序列中每个周期的长度和对称中心的位置不同，将对称周期序列分为4种情况，并分别研究它们在图象子带编码中的对称扩展方法。实验结果表明，按这种对称扩展方法能使重构信号在边界处不存在任何失真。

In a subband image coding system, due to the non ideal characteristics of the analysis/synthesis filters and the decimation/interpolation operations, the reconstructed signal, in general, suffers from magnitude/phase distortions and aliasing errors. For finite length sequences (e.g. the image signals), besides the above errors, there is an additional error--the expansive effect around the borders due to linear convolution. Though the conventional symmetric extension and circular convolution are applied, the experiments show that the border distortion still exists in the reconstructed signal. The symmetric extension method is further studied in this paper and extended to the M channel linear phase perfect reconstruction filter banks. In this paper, different symmetric sequences are formulated in a unified form based on the circular symmetry framework. According to the period and the symmetric center of symmetric periodic sequences, four permissible types of symmetric extension are derived. The experiment shows that the reconstructed signal is free from distortion.