Equal ripple amplitude and maximally flat group delay digital filters

In this paper we discuss a new class of hybrid IIR/ FIR digital filters. These filters present a maximally flat group delay in the given passband and an equiripple nature in the magnitude response both in the passband and in the stopband(s). The all-pole IIR component is synthesized so that its group delay exhibits a maximally flat behaviour in the pass-band 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, band-pass and highpass. By suitably optimizing the maximum value 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 passband is narrow (of the order of .1π or smaller) and a rather sharp cutoff is required. The performance of these filters is, however, slightly worse that obtainable with corresponding filters having equiripple group delay [1]. Several comparisons between different filter types are presented.