Frequency estimation from crossings of an observed mean level

Abstract

SUMMARY By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. If the mean level is unknown and estimated from the observed mean level, then this crossing estimator is more or less biased, depending on the length of the observation interval. It is shown that if the interval is at least two mean wavelengths, then the bias is small and of the same order as the standard deviation of a certain unbiased zero crossing estimator. Therefore the crossing method gives a simple and reliable technique for automatic estimation of the mean frequenoy of a process over long periods of time, which may involve changes in the mean level and covariance function.