The Performance of Analog Correlators with Linearly Delayed Inputs

The output mean and variance are determined for an analog cross correlator whose input signals have a delay which varies linearly with time. The output variance is seen to depend on the fourth-order expectation of the input signals. Examples are included to show how the varying delay could change the location of the correlation peak and, in some cases, give rise to multiple peaks. The output signal-to-noise ratio is defined as the ratio of the output mean to the output standard deviation, evaluated at the correlation peak. For the case of low-pass, white, Gaussian input signals, and a correla tor using an ideal integrator as averager, the output signal-to-noise ratio is plotted versus integration time for various combinations of delay rate and input signal-to-noise ratio. For a constant delay, the output signal to-noise ratio increases monotonically with integration time; but for nonzero delay rates, optimum integration times exist. Also, for fixed input signal-to-noise ratio, the output signal-to-noise ratio, at the optimum integration time, decreases with increasing delay rate.