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.