A posteriori time-varying filtering of averaged evoked potentials. I. Introduction and conceptual basis

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 he 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 time-invariant "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.