Recursive Nth-band digital filters- Part I: Design and properties

We investigate the properties of a special class of recursive polyphase filters whose subfilters are distinct allpass filters. On the basis of the discovered properties, a Remez-type algorithm is constructed for designing these filters. The proposed algorithm is faster and gives higher filter selectivities than other existing methods. Better understanding of the filter properties allows us to select the branch filter orders such that the filter complexity is minimized. In addition to nonlinear-phase filters, the algorithm is applicable to the design of approximately linear-phase filters. Several examples are included illustrating the efficiency of the proposed design scheme. The characteristics of the resulting filters are exposed by means of experimental results, and the implementation of the allpass branch filters is discussed. In a companion paper [33], we use these polyphase filters as basic building blocks in constructing efficient filters for sampling rate alteration. In addition, it is shown how the don't care bands, which cannot be avoided in filters of this type, can be suppressed by using an additional correction filter stage.