Multirate specifications via alias-component matrices

Alias-component (modulation) matrices permit systematic specification of multirate structures, and are easily incorporated into model-matching design procedures. In contrast, earlier methods for deriving multirate specifications may yield inappropriate structures. An example discussed here is the realization of a fractional L/M rate-changer as a cascade of upsampler-by-L, filter and downsampler-by-M, which is inappropriate for filterbanks that split the spectrum into rationally related bands. If the polyphase implementation of the rate changer is used, with L, M permitted to have common factors, then filterbanks that achieve arbitrary rational bandsplits are possible, as shown here. A corollary is that a multiband signal with rationally related bands can be sampled at the optimum Nyquist-Landau rate by appropriate choice of L and M.