ZERO-CROSSING RATES OF MIXTURES AND PRODUCTS OF GAUSSIAN-PROCESSES

Formulas for the expected zero-crossing rate of non-Gaussian mixtures and products of Gaussian processes are obtained. The approach we take is to first derive the expected zero-crossing rate in discrete time an d then obtain the rate in continuous time by an appropriate limiting a rgument. The processes considered, which are non-Gaussian but derived from Gaussian processes, serve to illustrate the variability of the ze ro-crossing rate in terms of the normalized autocorrelation function r ho(t) of the process. For Gaussian processes, Rice's formula gives the expected zero-crossing rate in continuous time as 1/pi root-rho ''(0) . We show processes exist with expected zero-crossing rates given by k appa/pi root-rho ''(0) with either kappa much greater than 1 or kappa much less than 1. Consequently, such processes can have an arbitrarily large or small zero-crossing rate as compared to a Gaussian process w ith the same autocorrelation function.