Higher-order spectrum in understanding nonlinearity in EEG rhythms
Summary: The fundamental nature of the brain's electrical activities recorded as electroencephalograms (EEG) remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEGs because of their robustness, simplicity of interpretation, and apparent association with the rhythmic behavioral patterns in nature. We extend the use of a higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extended Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, and therefore can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. This paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs) and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows the utility of bispectral methods as an analytical tool in understanding the neural processes underlying human EEG patterns.
scientific article; zbMATH DE number 6014115