Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 206857, 8 pages
Research Article

Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

1Medical Image Processing Lab, EPFL, 1015 Lausanne, Switzerland
2Department of Computer Science and Mathematics, K.N.S. Institute of Technology, Bangalore 560064, India
3MEG Core, National Institute of Mental Health, Bethesda, MD 20892, USA
4Department of Psychopharmacology, NIMHANS, Bangalore 560029, India

Received 2 October 2011; Accepted 27 October 2011

Academic Editor: Vikas Rai

Copyright © 2012 Cauchy Pradhan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG) remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of 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 extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The 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 utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.