Two design methods, namely method 1 and method 2, for class partial response FIR filters with equiripple stopband attenuation and low intersymbol interference (ISI) are investigated. For method 1, we design only a transmitter filter. For method 2, we design a transmitter and receiver filter pair having nearly the same amplitude response in the frequency domain. Both design methods have mainly three steps in common. First, a truncated sampled sequence of an ideal impulse response is used as an initial impulse response of the filter or filter pair in cascade. The optimum length of the sequence is examined. Second, z is transformed into such that the stopband section on the z-plane unit circle of the filter is mapped to be the entire unit circle in the -plane. Then a special all-zero function of is constructed having equiripple amplitude response along the unit circle. From this function, the filter transfer function of z with equiripple stopband attenuation is derived by inversely transforming into z. Finally, zero ISI approximation is performed with least-squares criterion, which drastically reduces ISI without significant change in the attenuation. Various characteristics of the filters designed by both methods are also illustrated.

A method of designing digital FIR transmitter and receiver filter pairs for classes and partial response systems is presented. The truncated ideal impulse response of a specified class is used as an initial response of the filter pair in cascade. For class I filter, the impulse response has an even symmetry, then its transfer function is a linear phase lowpass function of case 1 or case 2. Therefore, the passband zeros occur in mirror image quadruplet (and doublet) and the stopband zeros occur on the unit circle. The initial stopband attenuation slopes gradually up as frequency increases. To get an equiripple stopband attenuation for both filters, the passband zeros inside and outside the unit circle are assigned to transmitter and receiver filters respectively, then the stopband zeros of each filter are redetermined. Both filters form a matched filter pair. Next, the passband zeros of the filter pair are adjusted to give minimum intersymbol interference (ISI) in the overall response. For class filter, the impulse response has an odd symmetry and its transfer function is a linear phase lowpass function of case 3. In this case, the filter pair are designed to have equiripple and nearly the same stopband attenuation. Zero ISI approximation is performed similarly. Two design examples are shown. One is a 57th order class I filter pair having 0.05% ISI. The other is 61st order transmitter and 57th order receiver class filter pair whose ISI is 0.2%.