Phase inversion and 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 conditions where the detection of the desired signal using cross-spectral fails partially or entirely in the presence of a second uncorrelated signal. Not understanding when and how this effect occurs can lead to dramatic underreporting of the desired signal. Theoretical, simulated and experimental demonstrations of this effect as well as mitigating methods are presented.