Digital filters with equiripple magnitude and group delay

This paper introduces a class of recursive digital filters having equiripple behavior in both the magnitude and group delay responses. The filters consist of an all-pole IIR component cascaded with a linear phase FIR component. The IIR component is synthesized so that its group delay exhibits an equiripple variation in the passband, whereas the FIR component is used to obtain the desired equiripple nature for the amplitude response in both the passband and stopband(s). An iterative procedure is presented for optimizing the ripple in the group delay and the order of the IIR part in such a way that the overall multiplication rate attains its minimum. Examples show that standard simultaneous amplitude and phase optimization methods only slightly change the results obtained using this method. The new method is straightforward to implement and avoids the problems of guessing good initial values and of premature termination. Several examples show that the new filters require significantly fewer multipliers in narrow-band applications than equivalent FIR and delay equalized elliptic designs at the expense of a negligible variation in the group delay.