ABSTRACT
A discrete process is a purely random process if the random variables (rvs) are a sequence of mutually independent and identically distributed (id) variables. The sample space, the probabilities of each outcome, and the sequences constitute a discrete-time stochastic process or random sequence. Since the author is unable to produce ensemble averages in practice, he is left with only one realization of the stochastic process. To overcome this difficulty, assume that the process is ergodic. The relationship also applies for all statistical characteristics such as mean value, variance, correlation, etc. If the relationship is true for any number of rvs of the time series, then the process is known as strictly stationary process. The number of realizations increases, the mean tends to zero and the autocorrelation tends to a delta function, as it should be. Linear time-invariant filters are used in many signal processing applications.
