Effect of Record Length on Noise-Induced Error in the Cross Correlation Estimate

There is a continuing increase in the use of correlation in engineering. In these applications some or all of the signals to be analyzed may be obscured by noise. Since determination of the autocorrelation or cross correlation requires knowledge of the signals for all time, one must use the observed signals to obtain an estimate of the desired correlation function. These estimates, autocorrelograms or crosscorrelograms, are affected when the signal is obscured by noise. A theoretical investigation of the noise-induced error in correlograms is presented. It is shown that the rms error is inversely proportional to the square root of the record length for virtually any noise which might be encountered. This provides a guide for the reduction of the noise error to any desired level. In addition, bounds on the error are determined for some more common types of noise. Experimental results are described which verify the theoretical developments. The theoretical results are applied to a study of the transmission of action potentials through the cockroach ganglion.