Recursive Nth-band digital filters- Part II: Design of multistage decimators and interpolators

In a companion paper [1], an efficient procedure was given for the design of recursive polyphase filters whose subfilters are distinct allpass filters, and the properties of these filters were considered in detail. Both nonlinear-phase and approximately linear-phase filters were discussed. In this paper, we show how these filters can be used for constructing efficient single-stage and multistage decimators and interpolators. The resulting designs suffer from the inherent limitation that aliasing cannot be prevented into the transition band in the decimation case. It is shown how this limitation can be overcome by using an additional filter stage at the output of the decimator. Working at the lowest sampling rate, this filter increases only slightly the overall computation rate. The optimization of this filter stage, together with the actual decimation stages, is discussed in detail in both the nonlinear-phase and approximately linear-phase case. Several examples illustrate the efficiency of the new overall designs compared to other known decimators and interpolators.