Stochastic Sampling of a Binary Random Process

When a binary random process is sampled by an independent random pulse process a new binary process is generated. Statistical properties of this new binary process are investigated in this paper. Two methods of sampling are considered, according as an even or odd number of zeros of the binary process being sampled occur between successive sampling pulses. When the binary process is one in which the number of zeros in a given time interval obeys the Poisson distribution, and the time intervals between successive sampling pulses are independent, then the time intervals between successive zeros of the output binary process are also statistically independent, in which case all statistical properties of the output process are obtained. By iteration of this sampling procedure it is shown that a whole class of binary random processes, all having statistically independent intervals, is made accessible. The autocorrelation function of the output binary process is obtained in the case where an arbitrary binary process is sampled by a pulse process having independent intervals. The mean rate of the output process is discussed when the sampling intervals are not independent. Four special cases are considered as examples. Finally a brief description of an experimental sampling device and some results obtained with it, is given. This paper is envisaged as the first of a series of three papers dealing with binary random processes and their application in the analysis of simple filters containing a randomly switched parameter.