Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Cepstrum of bispectrum-A new approach to blind system reconstruction
Signal Processing
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The nature of nonlinear interaction has hardly been addressed for a complex signal like electroencephalogram (EEG). In this paper we use of higher-order spectrum to elucidate the hidden characteristics of EEG signals that simply do not arise of 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 present Hinich's bispectral measures for EEG signals during seizure, sleep and in the state of anesthesia and contrast these with that of the normal brain rhythms of alpha, beta, theta delta and indeterminate EEG activities. The squared bicoherence in the non-redundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are found to be 2.71± 0.8544 in case of generalized seizure. The deep (NREM stage 4) shows similar range of bicoherence values (2.336 ± 0.658). In contrast to the non-REMphases, the fast activity REM sleep reveals a lower bicoherence (1.99 ± 0.613). During anesthesia the bicoherence values is reduced to 1.696 ± 0.7686. The consciousness is grossly affected during, seizure, deep sleep and anesthesia. Therefore, bicoherence has implications in understanding level of consciousness of the brain. The results carry implications in understanding neurobiological processes in epilepsy, sleep and anesthesia. The results of the study reemphasizes the utility of bispectral methods as an analytical tool in understanding neural process brain functioning.