Abstract
This paper forms a preface and introduction to a new method for the estimation of evoked potentials: a posteriori time-varying filtering. A simple evoked potential model, consisting of a transient signal and additive noise, is discussed and the underlying assumptions explicitly formulated. Assuming this model, the problem of estimating the signal from an ensemble is considered from the statistical and communication engineering point of view, along with a brief survey of the pertinent literature. It is explained why ensemble averaging, in general, does not provide the best estimate in the mean-square error sense. After a summary of the controversial aspects of timeinvariant “a posteriori ‘Wiener’ filtering”, it is indicated how that method can be generalized to a time-varying counterpart, which is able to handle the essentially transient character of evoked potential waveforms. Finally, the new method is presented on a conceptual level and its application illustrated by examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aunon, J.I., Sencaj, R.W.: Comparison of different techniques for processing evoked potentials. Med. Biol. Eng. Comput. 16, 642–650 (1978)
Basar, E., Gönder, A., Özesmi, C., Ungan, P.: Dynamics of brain rhythmic and evoked potentials. I. Some computational methods for the analysis of electrical signals from the brain. Biol. Cybern. 20, 137–143 (1975)
Bendat, J.S.: Principles and applications of random noise theory, Chaps. 4 and 9. New York: Wiley 1958
Blum, M.: Generalization of the class of nonrandom inputs of the Zadch-Ragazzini prediction model. IRE Trans. Inf. Theory IT 3, 76–81 (1956)
Cigánek, L.: Variability of the human visual evoked potential: normative data. Electroencephalogr. Clin. Neurophysiol. 27, 35–42 (1969)
Davis, R.C.: On the theory of prediction of nonstationary stochastic processes. J. Appl. Phys. 23, 1047–1053 (1952)
Doyle, D.J.: Some comments on the use of Wiener filtering for the estimation of evoked potentials. Electroencephalogr. Clin. Neurophysiol. 38, 533–534 (1975)
Efron, B., Morris, C.: Empirical Bayes on vector observations: an extension of Stein's method. Biometrika 59, 335–347 (1972)
Efron, B., Morris, C.: Stein's estimation rule and its competitors-an empirical Bayes approach. J. Am. Stat. Ass. 68, 117–130 (1973)
Efron, B., Morris, C.: Sten's paradox in statistics. Sci. Am. 236, 5, 119–127 (1977)
Gabor, D.: Theory of communication. J. I.E.E. 93, 429–457 (1946)
Gasser, Th., Rosenblatt, M.: Smoothing techniques for curve estimation. Workshop proceeding, In: Lecture Notes in Mathematics, Vol. 757. Berlin, Heidelberg, New York: Springer 1979
Gasser, Th., Weingärtner, O., Verleger, R.: ROSMO: a method for estimating event-related potentials (to appear, 1981)
Hampel, F.R.: The influence curve and its role in robust estimation. J. Am. Stat. Ass. 69, 383–393 (1974)
Hartwell, J.W., Erwin, C.W.: Evoked potential analysis: on-line signal optimization using a mini-computer. Electroencephalogr. Clin. Neurophysiol. 41, 416–421 (1976)
James, W., Stein, C.: Estimation with quadratic loss. In: Proc. Fourth Berkeley Symp. Math. Stat. and Prob., Vol. 1. Neyman, J. (ed.), pp. 361–379. Berkeley: University of California Press 1961
Kearney, R.E.: Evaluation of the Wiener filter applied to evoked EMG-potentials. Electroencephalogr. Clin. Neurophysiol. 46, 475–478 (1979)
Lee, Y.W.: Statistical theory of communication, Chap. 17. New York: Wiley 1960
McGillem, C.D., Aunon, J.I.: Measurements of signal components in single visually evoked brain potentials. IEEE Trans. Biomed. Eng. 24, 232–241 (1977)
Middleton, D.: An introduction to statistical communication theory, Chap. 1. New York: McGraw-Hill 1960
Nagelkerke, N.J.D.: Personal communication (1979)
Nagelkerke, N.J.D., Strackee, J.: Some notes on the statistical properties of a posteriori Wiener filtering. Biol. Cybern. 33, 121–123 (1979)
Papoulis, A.: Signal analysis. New York: McGraw-Hill 1977
Pfurtscheller, G., Cooper, R.: Selective averaging of the intracerebral click evoked responses in man: an improved method of measuring latencies and amplitudes. Electroencephalogr. Clin. Neurophysiol. 38, 187–190 (1975)
Stein, C.: Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In: Proc. Third Berkeley Symp. Math. Stat. and Prob., Vol. 1. Neyman, J. (ed.), pp. 197–206. Berkeley: University of California Press 1955
Strackee, J., Cerri, S.A.: Some statistical aspects of digital Wiener filtering and detection of prescribed frequency components in time averaging of biological signals. Biol. Cybern. 28, 55–61 (1977)
Strackee, J.: Averaging for signal and parameter estimation (abstract). Proc. XII Int. Conf. Med. Biol. Eng., Part IV (1979)
Ungan, P., Basar, E.: Comparison of Wiener filtering and selective averaging of evoked potentials. Electroencephalogr. Clin. Neurophysiol. 40, 516–520 (1976)
Wahba, G., Wold, S.: Periodic splines for spectral density estimation: the use of cross-validation for determining the degree of smoothing. Comm. Stat. 4, 125–141 (1975)
Walter, D.O.: A posteriori “Wiener filtering” of average evoked responses. Electroencephalogr. Clin. Neurophysiol. Suppl. 27, 61–70 (1969)
Wastell, D.G.: Statistical detection of individual evoked responses: an evaluation of Woody's adaptive filter. Electroencephalogr. Clin. Neurophysiol. 42, 835–839 (1977)
Wastell, D.G., Kleinman, D.: N1-P2 correlates of reaction time at the single-trial level. Electroencephalogr. Clin. Neurophysiol. 48, 191–196 (1980)
de Weerd, J.P.C., Martens, W.L.J., Colon, E.J.: Estimation of evoked potentials using time-varying Wiener filtering (abstract). Electroencephalogr. Clin. Neurophysiol 43, 476–477 (1977)
de Weerd, J.P.C., Martens, W.L.J.: Theory and practice of a posteriori “Wiener” filtering of average evoked potentials. Biol. Cybern. 30, 81–94 (1978)
de Weerd, J.P.C., Kap, J.I.: Spectro-temppral representations and time-varying spectra of evoked potentials. A methodological investigation. Biol. Cybern. 41, 101–117 (1981a)
de Weerd, J.P.C., Kap, J.I.: A posteriori time-varying filtering of averaged evoked potentials. II. Mathematical and computational aspects. Biol. Cybern. 41, 223–234 (1981b)
Wiener, N.: The extrapolation, interpolation, and smoothing of stationary time series, with engineering applications. New York: Wiley 1949
Woody, Ch.D.: Characterization of an adaptive filter for the analysis of variable latency neuroelectric signals. Med. Biol. Eng. 5, 539–553 (1967)
Zadeh, L.A., Ragazzini, J.R.: An extension of Wiener's theory of prediction. J. Appl. Phys. 21, 645–655 (1950)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Weerd, J.P.C. A posteriori time-varying filtering of averaged evoked potentials. Biol. Cybern. 41, 211–222 (1981). https://doi.org/10.1007/BF00340322
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00340322