Bicoherence analysis of nonstationary and nonlinear processes

TL;DR

This paper extends bicoherence analysis to nonstationary signals, proposing a filtering method to reduce false positives and improve detection of true quadratic nonlinearities in time-varying processes.

Contribution

It generalizes bicoherence analysis for nonstationary signals and introduces a step-by-step filtering method to mitigate false positives in nonlinear coupling detection.

Findings

The method effectively reduces false positives in nonstationary signal analysis.

Demonstrated on physics-based numerical systems with clear results.

Applicable to various coherence calculations beyond bicoherence.

Abstract

Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic bicoherence, unfortunately, tends to give false positives -- high bicoherence values without actual nonlinear coupling of different frequency components -- for signals exhibiting rapidly changing amplitudes and limited length. The effect of false positive values can lead to misinterpretation of results, therefore a more prudent analysis is necessary in such cases. This paper analyses the properties of bispectrum and bicoherence in detail, generalizing these quantities to nonstationary processes. A step-by-step method is proposed to filter out false positives at a given confidence level for the case of nonstationary signals. We present a number of test cases, where the method is demonstrated on simple physics-based numerical systems. The approach and methodology introduced in the paper can be generalized to lower and higher order coherence calculations.