IIR filters with reduced multipliers using cyclotomic polynomial numerators

A method to design rotational polynomial efficient infinite impulse response (IIR) digital filters with unit circle zeros is presented. The authors employ a prefilter-equalizer method, using cyclotomic polynomial building blocks to form a finite impulser response (FIR) multiplierless prefilter (numerator) to provide stopband attenuation. The linear methods of Jackson and Lemay (1990) are then used to design the all-pole equalizer (denominator) portion of the prefilter-equalizer cascade, such that the passband is equiripple. Examples show that substantial savings in the number of multipliers are achieved when compared to the complexities of minimum-order elliptic filters meeting the same specifications