Non-gaussianity and non-linearity in electroencephalographic time series

  • Th. Gasser
  • G. Dumermuth
Part II: Research Reports
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)


In this interdisciplinary contribution we discuss a number of problems related to stochastic models and statistical methods used in electroencephalography. The main part of the paper is devoted to the assumption of a Gaussian process. We present a variety of methods to check empirically such an assumption, together with examples. The deviations from a Gaussian process which occur in EEG analysis are interpreted in terms of non-linear dynamics; the input-output-map is assumed to be well represented by a Volterra series.


Gaussian Process Volterra Series Inverse Filter High Order Spectrum Complex Demodulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math. 22, 203–17Google Scholar
  2. Bingham, C., M.D. Godfrey, J.W. Tukey (1967). Modern techniques of power spectrum estimation. IEEE Trans. Audio Electroac. AU-15, 56–66Google Scholar
  3. Brillinger, D.R. (1970). The identification of polynomial systems by means of higher order spectra. J. Sound Vib. 12, 301–313Google Scholar
  4. Brillinger, D.R. (1975). Time series analysis. Holden-Day, San Francisco.Google Scholar
  5. Brillinger, D.R., M. Rosenblatt (1967). Asymptotic theory of estimates of k-th order spectra. Spectral Analysis of Time Series, 153–186, ed. B. Harris, J. Wiley, New YorkGoogle Scholar
  6. Cooley, J.S., J.W. Tukey (1965). An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 267–301Google Scholar
  7. Dumermuth, G., P.J. Huber, B. Kleiner, T. Gasser (1971). Analysis of the interrelations between frequency bands of the EEG by means of the bispectrum. Electroenceph. Clin. Neurophysiol. 31, 137–148Google Scholar
  8. Dumermuth, G., Th. Gasser, B. Lange (1975). Aspects of EEG analysis in the frequency domain, CEAN, ed. G. Dolce & H. Künkel, 429–457, G.Fischer StuttgartGoogle Scholar
  9. Gasser, Th. (1977). General characteristics of the EEG as a signal. EEG-Informatics, ed. A. Rémond, 37–52, Elsevier/North Holland, Amsterdam.Google Scholar
  10. Gevins, A.S., Ch.L. Yeager, S.L. Diamond, J.P. Spire, G.M. Zeitlin, A.H. Gevins (1975). Automated analysis of the electrical activity of the human brain. Proc. IEEE, 63, 1382–1399Google Scholar
  11. Lopes da Silva, F.H., A. Dijk, H. Smits (1975). Detection of non-stationarities in EEG using the autoregressive model. CEAN, ed. G. Dolce & H. Künkel, 180–199, G. Fischer, StuttgartGoogle Scholar
  12. Marti, J.T. (1971). On the approximation of continuous non-linear operators in normed spaces by polynomial operators, ZAMP 22, 991–996Google Scholar
  13. Rozanov, Y. (1967). Stationary stochastic processes. Holden-Day, San Francisco.Google Scholar
  14. Wiener, N. (1958). Non-linear problems in random theory. Cambridge, MIT-PressGoogle Scholar
  15. Zetterberg, L.H. (1969). Estimation of parameters for a linear difference equation with application to EEG-analysis. Math. Biosci. 5, 227–275Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Th. Gasser
    • 1
  • G. Dumermuth
    • 1
  1. 1.Universitäts-KinderklinikZürich

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