Optimization of an improved Nyquist filter with piece-wise polynomial frequency characteristic

In this paper, we optimize an improved Nyquist pulse generated by CC3 filter with piece-wise parabolic frequency characteristic. Its asymptotic decay rate is t^-2. The Nyquist pulse optimized here has a closed-form expression in time domain. Its performance is superior to previously reported pulses when sampled with a time offset. The optimization of the pulse was performed using Nelder-Mead method in order to minimize the symbol error probability. We have considered a timing offset that takes values between 0 and 0.3 and have determined the optimal values of the parameter value b as a function of the excess bandwidth α, given an imposed value of the parameter m that results from practical reasons.