Optimal a posteriori time domain filter for average evoked potentials

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Abstract
Evoked potentials measured with scalp electrodes are often described as a deterministic process corrupted by unrelated noise. The common procedure to determine the signal is to average N repetitive measurements. By obtaining additional information from the N measurements, signal detection can be improved. An algorithm that estimates the signal autocorrelation from N given measurements is proposed. The estimator is consistent and unbiased, and its variance tends to 0 as o(N). Two filters that are applied to the average response are introduced. Both depend on the estimation of the signal and the noise autocorrelations. One filter is based on the assumption that the average response is a stationary process. The second filter coefficients are obtained by minimizing the mean squared error (MSE) of an optimal filter of a nonstationary process applied on a single sweep. When a small number of sweeps are averaged, the stationary assumption is adequate, and the MSE of the stationary optimal filter is two to five times less than the MSE of the average response. When a large number of measurements are considered, the error in estimating the autocorrelations decreases. In this case, applying the optimal filter for a nonstationary process leads to a significant improvement in the signal estimation.

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