The zero crossing variance of the smoothed random telegraph signal

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Abstract
The problem of determining the variance of the number of zeros in an interval (0, T) of an RC-filtered random telegraph signal is considered. We obtain an infinite series representation for the variance in terms of two parameters. When one of these parameters is an integer, the series reduces to a finite summation. Recursion relations for computation of the series terms are given, and the asymptotic behaviour of the variance is investigated. Finally, curves for the variance arc obtained for variations over four orders of magnitude of the two parameters.