Support constraints for M-band alias-free filter banks

A new formulation of the system equations that describe the behavior of the one-dimensional M-band maximally decimated analysis/synthesis filter bank system is presented. The development incorporates the effects of the shift-varying nature of the upsampling and downsampling operations. By explicitly including the filter regions of support, one is able to derive a more general expression for the relationships that must exist between the analysis and synthesis filters in order to cancel all interband aliasing. From this expression one can find (1) the M^M-1 distinct sets of analysis and synthesis filters from which an M-band alias-free filter bank can be constructed, and (2) the constraints on how these filters, once designed, can be shifted without destroying their aliasing cancellation properties