Design of IIR nyquist filter pairs with equi–ripple stopband attenuation

Abstract

AbstractThis paper deals with a design of digital transmitter and receiver IIR Nyquist low‐pass filter pairs for data transmission. The transmitter and receiver filters are required to limit the spectrum bandwidth of a transmitting signal and a received signal, respectively, and to have zero intersymbol interference when the filters operate in a cascade. Due to the bandlimiting requirements, the sampling frequency Fs = 1/Ts for the filters must be larger than twice the data transmission rate 1/T. This paper supposes the receiver filter followed by the time domain equalizer. The filter design proceeds as follows: first, the transmitter and receiver filters are designed to have the same transfer function with a stopband equiripple attenuation, considering the amplitude characteristics only. The filter transfer function is designed by using s – z transformation of the known analog elliptic filter, realizing the transition band characteristics with the preassigned roll‐off factor. The method does not require any iterative approximation. Secondly, the output of the receiver filter is decimated to the data symbol repetition rate T, then equalized in the time domain. The time domain equalizer consists of a linear or a decision feedback circuit, using an MS adaptive algorithm. The amount of delay given to the training signal supplied to the equalizer affects the residual errors. Let the order of the equalizer (numerator and denominator has the same order) denoted by n. Then an optimum delay is found to be equal to nT for the linear feedback circuit and (n/2)T for the decision feedback circuit.