ISI-free pulse with piecewise exponential frequency characteristic

A new parametric family of Nyquist ISI-free pulses denoted as Piecewise Flipped-Exponential (PFE) is proposed and investigated in terms of error probability when affected by symbol timing jitter. The proposed pulses use only two design parameters and ensure superior or equal performance compared to the previously reported pulses. The filter design is facilitated by the fact that the optimal value of one parameter is constant for a specified value of excess bandwidth, while the other one shows a cubic relationship with timing offset. We prove the feasibility of the new PFE pulses and illustrate its performance in term of ISI error probability, highlighting key trade-offs. In addition, we discuss and compare the practical implementation details of generating truncated/causal realizations of the filter including its square root response. The PFE pulses are compared with Harris–Moerder pulses that were designed in order to show zero spectral re-growth. The PFE pulses are superior to Harris–Moerder pulses in terms of error probability if timing jitter is present but are outperformed in terms of spectral re-growth.