A class of complementary IIR filters

A class of complementary IIR filters is introduced. One of these filters can be realized as a tapped cascaded interconnection of identical allpass subfilters. The complementary filter is then obtained automatically by adding some extra allpass subfilters and a subtractor. The proposed filters are always allpass complementary and, under certain conditions, also magnitude complementary. Further, in terms of the frequency selectivity, they exhibit properties similar to those of complementary linear-phase FIR filters. These properties are retained also after coefficient quantization. The design of the filters is divided into design of a prototype FIR filter and a prototype IIR filter being realizable as a parallel connection of two allpass filters. Design examples are included for demonstration.