Analysis of timing sensitivity and Nyquist pulse design

Pulse transmission through a band-limited channel without intersymbol interference is governed by the Nyquist criterion. A particular pulse that has been widely used in practice corresponds to the raised cosine spectrum. This paper addresses the question of how to generate other Nyquist pulses. A worst case design criterion from the literature for analyzing pulse sensitivity to timing errors is reviewed and extended. Closed form expressions are derived for the Nyquist pulse generating a pulse with a triangular rolloff spectrum. The error performance, versus excess bandwidth, of the triangular pulse is compared with that of the standard raised cosine pulse. The triangular pulse is found to outperform the raised cosine pulse.