Implicit averaging and delay determination of random binary waveforms

It is shown that for a broad class of random binary processes, the mean of a binary process, conditioned on its zero crossings, is proportional to the derivative of the correlation function of that process. This specific mean, referred to as the implicit mean, can be used both to characterize a random binary waveform and to determine its delay. The proposed empirical estimator of the implicit mean is unbiased, and its variance depends on the number of selected trajectories of the waveform being processed and the correlation between those trajectories.