Output Probability Density Functions for Cross Correlators Utilizing Sampling Techniques

Sampling techniques provide a practical means of obtaining cross-correlation functions. In this paper, the correlation function is described by sums of the form Z = \begin{equation*}Z = \Sigma^{N}_{j=1}X_{j}Y_{j}\end{equation*}. A general expression is derived for the probability density function of the random variable Z under the condition that Xj and Yj are stationary, jointly Gaussian random processes with nonzero means and unit variances.