On Designing PAM Pulses Optimally Tolerant to Timing Jitter

This paper deals with the design of bandlimited baseband PAM pulses that are optimally tolerant to timing jitter in a maximally flat sense. In this design the bandwidth can be chosen arbitrarily. The resulting time responses are relatively insensitive to small amounts of timing jitter and so represent an optimal solution for this type of impairment. Analytic results are derived in the frequency domain after translating conditions on maximal flatness from the time domain into the frequency domain by means of the Poisson sum formula.