The probability density function for the output of a cross-correlator with bandpass inputs

A general expression is derived for the probability density function of the output of a cross-correlator, the inputs of which are assumed to consist of deterministic signals with a common frequency plus correlated stationary Gaussian noises. The correlator is composed of input bandpass filters, a multiplier, and postmultiplier low-pass filter. The general expression for the density function is later reduced to some special cases for comparison with previous results. Prior treatments of the problem, however, have omitted the case of correlated noise inputs except under more restrictive conditions.