Stochastic Sampling of a Binary Random Process--II

A sampling scheme is considered in which a binary process with statistically independent axis-crossing intervals is sampled according to a given logic by a Poisson pulse process, thereby producing a new binary process. The results derived supplement the results of a previous paper on the sampling of a binary process by a random pulse process. The probability density of the time interval between successive zeros of the resulting binary process is derived, and it is shown how higher-order time interval statistics may be obtained. As an example, a periodic binary process is sampled by a Poisson pulse process, and it is shown that the first-order time interval density function of the resultant process is multimodal, which under certain limiting conditions becomes a symmetric density function.