Design of FIR partial response filters with equiripple stopband attenuation (class II, V)

Abstract

AbstractThis paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission. the filters are required to band‐limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero‐cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear‐phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1. percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman‐Schuessler design method for the minimum phase‐shift filter in the frequency domain, the transfer function is derived.To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI.