ZERO-CROSSING INTERVALS OF RANDOM PROCESSES

Abstract
This report describes a digital system for studying the zero crossing intervals of random processes. Probabilities and probability densities defined by the zero crossing points of various Gaussian processes are presented. Probabilities and probability densities defined by the zero-crossing points of a random process consisting of a sine wave plus a Gaussian process are also presented. Finally probabilities and probability densities defined by the stationary points of a random process consisting of a sine wave plus a Gaussian process are presented. At present none of the probabilities or probability densities can be derived explicitly by analytical methods. The standard deviations associated with the probability densities are also presented. In the case of the Gaussian processes the correlation co-efficients for two successive Intervals are presented. The first moments associated with the probability densities are compared with the exact theoretical values. All the other experimental results are compared with theoretical approximations. The statistical dependence between the ith zero-crossing interval and the (i+n)th zero-crossing interval is investigated.

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