Equal ripple amplitude and group delay digital filters

In this paper we discuss a new class of hybrid IIR/ FIR digital filters. These filters present equiripple behaviour both in the magnitude and group delay responses. The all-pole IIR component is synthesized so that its group delay exhibits an equiripple variation in the passband whereas the linear phase FIR component is used to obtain the desired equiripple nature in the amplitude response both in the passband and stopbands. The filter types handled are lowpass, bandpass and highpass. By suitably optimizing the ripple in the group delay and the order of the IIR component we obtain filters requiring significantly fewer multipliers than equivalent FIR and group delay equalized elliptic designs when the pass-band is narrow (of order .1π or smaller) and a rather sharp cutoff is required. Examples illustrating this feature are presented in the paper.