Phase inversion and collapse of the cross-spectral function

TL;DR

This paper investigates the limitations of cross-spectral analysis in detecting correlated signals when uncorrelated signals interfere, revealing conditions that cause detection failure and proposing mitigation strategies.

Contribution

It identifies specific conditions leading to the collapse of the cross-spectral function and demonstrates this effect through theory, simulations, and experiments, providing insights for more reliable analysis.

Findings

Cross-spectral analysis can fail under certain uncorrelated signal conditions.

The paper demonstrates the effect through theoretical, simulated, and experimental methods.

Mitigation strategies can reduce the impact of these failures.

Abstract

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.