A posteriori time-varying filtering of averaged evoked potentials. II. Mathematical and computational aspects

Abstract

The problem of estimating an unknown transient signal, given an ensemble of waveforms, in which this signal appears as a nonrandom component in the presence of additive noise is considered. This problem is solved by generalizing the method of "a posteriori 'Wiener' filtering". In the new method, the ensemble average is filtered by a time-varying system which is based on estimated time-varying power spectra of signal and noise. The nature of this system, and the computational procedures involved, are discussed in detail. A software package for time-varying filtering is briefly described. Application of the method is illustrated by a simulation example, which also provides a comparison to time-invariant a posteriori "Wiener" filtering.