Optimization of a square-root Nyquist filter with staircase frequency characteristic

In this paper, we optimize a square-root Nyquist pulse with an asymptotic decay rate of t^-1 produced by an Nyquist filter with a staircase frequency characteristic. The performance of new inter-symbol interference free pulses and the squared root filter are studied with respect to the ISI error probability, in the presence of a timing error. To illustrate the achieved improvement, the new family of pulses is compared with some recently proposed pulses. Both the staircase Nyquist pulse and the one produced by the square root filter have a closed form expression in time domain and outperform most previously reported pulses in several cases of commonly considered benchmark tests.