Collapse of the cross-spectral function

Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of amplitude and phase conditions where the detection of the desired signal using cross-spectral analysis fails partially or entirely in the presence of a second uncorrelated signal [1-2]. Not understanding when and how this effect occurs can lead to dramatic under-reporting of the desired signal.