Efficient FIR, IIR, and hybrid nyquist filters with zero intersymbol interference

This paper extends the recently introduced class of multistage FIR Nyquist filters to cover also the multi-stage IIR and hybrid IIR/FIR Nyquist filters. The filter stages, as well as the overall system, have zero intersymbol interference. The filter stages are simultaneuosly designed to provide a Chebyshev stopband behavior for the overall filter, thereby band-limiting the pulses optimally. Computationally efficient IIR filter stages are obtained by using the polyphase structure with allpass subfilters. Selecting one of the subfilters to be a pure delay results in zero intersymbol interference. Efficient procedures are presented for simultaneously optimizing the filter stages for both IIR and hybrid IIR/FIR cases. Examples demonstrate how the proposed multistage IIR filters provide significant advantages over other existing IIR designs and a slight reduction in the multiplication rate compared to multistage FIR designs.