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For general assumptions concerning bandpass signal and noise inputs, previous analyses of analog cross correlators have yielded very complicated expressions for the probability density function (pdf) of the correlator output. The inherent computational difficulties, therefore, limited the application of these pdf's almost exclusively to special cases of equal noise powers and noise spectrums symmetric about the signal's frequency. In this correspondence it is shown that for general bandpass inputs, the correlator output can always be expressed as the difference of two scaled independent noncentral chi-squared variables if a certain matrix transformation of variables is employed. The characteristic function method is then used to derive the pdf, which is as readily computed as for the case of special assumptions.