Generalized averaging and noise levels in evoked responses.

A formal relationship between the mean square noise level in an evoked potential experiment, the number of averages and the autocorrelation function of the noise is derived. The generalized averaging process is recast as a filter applied to the noise signal. This filter is computed for a number of different types of evoked potential experiments in which various weighting factors and stochastic stimulation times are allowed. Although the variance in noise level estimates can be large, there is a general trend for noise reduction to occur more slowly than the expected 1/N when the total time over which averaging occurs is small in comparison to the correlation time of the noise. When the total averaging time exceeds the temporal extent of the autocorrelation function, the expected 1/N behavior is observed.