The linear filtering of separable processes

Abstract

From an extension of the predictive property of separable random processes it is shown that the output from a linear filter, when subjected to a signal of this class as input, remains a separable process. The conditions are determined for the generation of separable processes having any prescribed power spectrum and for the summation of separable processes into a single separable process. The output from a linear filter subjected to an nth-order separable process is also shown to be a separable process of the same order.