Effect of cross-correlation on auditory evoked response detection

A procedure to quantify the relationship between the signal-to-noise ratio (SNR) and the number of observed series of the auditory brainstem response is discussed. The commonly held belief that the SNR increases as the number of terms being averaged originates from the assumption that repeated series of the evoked potential are perfectly correlated. It is shown that in practice the correlation is far from perfect and this leads to an underestimate of the number of observations which are required to obtain a desired SNR. The presented formula quantifies this dependency for all values of the cross-correlation between series, and reduces to the accepted form for perfectly correlated signals