Analysis filters´ symmetry polarities of M-channel alias-free linear-phase filter banks

The choice of analysis filters´ symmetry polarities is a key factor and difficult problem to the design of M-channel alias-free linear-phase filter banks (AFLPFB) due to only error-and-trial method available for some special cases. This paper is devoted to conquer the puzzle and the general methods are proposed through theoretical analysis and derivation. The results show that the invented method agrees well with the special cases with M less than 3 which were discussed in literatures, and can be applied to determine the analysis filters´ symmetry polarities of any M-channel linear-phase filter banks (LPFB)