Error characterization of duty cycle estimation for sampled non-band-limited pulse signals with finite observation period

In many applications the pulse duration of a periodic pulse signal is the parameter of interest. Thereby, the non-band-limited pulse signal is sampled during a finite observation period yielding to aliasing and windowing effects, respectively. In this work, the pulse duration estimation based on the mean value of the samples is considered, and an exact expression of the mean squared estimation error (averaged over all possible time shifts) is derived. The resulting mean squared error expression depends on the observation period, the pulse period and the pulse duration. Analyzing the effect of these parameters shows that the mean squared error can be reduced (i) if the observation period is a multiple of the pulse period, (ii) if the pulse period is not a multiple of the sampling period, and (iii) if the total number of samples is a prime number. All results were validated with simulation results.