On Level Crossing Excursions of Low-Pass Random Processes

Level crossing problems have been the subject of much study over the centuries. Practical applications can be found in many fields of engineering, e.g., predicting flood levels, random mechanical stress analysis, electrical excursions that overload equipment, and disruptive effects in signal processing. In this paper, we focus on stationary Gaussian low-pass random processes, and in particular, of the discrete-time first-order Markov type. We apply known results for continuous-time processes to arrive at a general understanding of the excursion statistics for discrete-time processes. Expressions are derived for the crossing rate, shape of large excursions, peak distribution, and sojourn probability. Simulation results are compared with the various continuous-time and discrete-time theoretical formulations.