A new IIR Nyquist filter with zero intersymbol interference and its frequency response approximation

A new infinite impulse response (IIR) Nyquist filter with zero intersymbol interference is proposed. The necessary and sufficient conditions for the transfer function are obtained. The proposed IIR Nyquist filter requires only frequency-domain optimization. Multistep optimization, using the iterative Chebyshev approximation, is proposed. This method is able to design a new kind of IIR Nyquist filter with the minimum order. Numerical examples for 30- and 15-percent rolloff rates are illustrated. From these examples, it is confirmed that the IIR approach can reduce the filter order and hardware size, compared with the conventional finite impulse response (FIR) Nyquist filters. Its efficiency becomes marked for high Nyquist filters.