The design of optimal multirate bandpass and bandstop filters

Narrow-band bandpass and bandstop filters are inherently of high order and require a large computation rate. A multirate filter using decimators and interpolators can be designed to have bandpass or bandstop characteristics, often with a much smaller computation rate. This paper develops rules for designing such a filter by placing constraints on the filter approximation error and the aliasing error. The question of admissible decimation factors is investigated in detail. A method to minimize the computation rate is described. Several examples are presented.