Relation between Analysis Filters´ Symmetry Polarities and Lengths of M-channel Alias Free Linear Phase Filter Banks

M-channel alias-free linear-phase filter banks (AFLPFB) include M linear-phase (LP) FIR analysis filters and have a LP distortion function. Linear-phase perfect-reconstruction filter banks (LPPRFB) are apparently a class of AFLPFB, and widely used in various applications. Although the filters´ symmetry polarities and lengths of analysis filters are studied in the literature, the relation between them is never revealed, thus the general method is not yet available up to date for choosing the filters´ symmetry polarities and lengths of M-channel LPPRFB. In this paper, for generality, the relation between the analysis filters´ symmetry polarities and lengths (RAFSPL) of M-channel AFLPFB is firstly derived, and according to which the relation among analysis filters´ lengths (RAFL) of M-channel AFLPFB is obtained. The results show that all LPPRFB reported so far follow our general method.