Some Results on the Analysis of Random Signals by Means of a Cut-Counting Process
Irwin Miller, John E. Freund · Journal of Applied Physics · 1956
The variance of the number of zeros of a Gaussian signal on a short time interval was derived in a recent paper by Steinberg, et al. This result is generalized to include the covariance of the number of zeros of a Gaussian signal at the values θ1 and θ2, using a somewhat different mathematical approach. A special case with θ1=θ2=θ gives the variance of the number of times the signal equals θ on a given time interval.