B.S.T.J. Briefs: Approximate and Exact Results Concerning Zeros of GaussianNoise

Let r denote the interval between two successive zeros of a stationary gaussian process having zero-mean and one-sided power spectral density TF(/). AVe shall refer to such an interval as a zero-crossing interval. This brief is concerned with these probability functions: (i) P0{T) = Probability density of a zero-crossing interval. (II) F0(T) = Probability that a zero-crossing interval lasts longer than T. Thus, F0(T) and P,,(r) are related by Fa(r) = £° P,,(x) dx = 1 - ( Po(x) dx. (1)