Correlation of Signals Having a Linear Delay
Winslow R. Remley · The Journal of the Acoustical Society of America · 1963
The output signal of a cross-correlation detector is calculated for a general signal spectrum and integration time under the assumption of a constant delay rate but otherwise ideal conditions. The delay-rate degradation of the output signal is shown to be equivalent to passing the ideal cross-correlation function through a low-pass filter. The output signal-to-noise ratio is evaluated for the threshold case by introducing straight-forward noise statistics. Subsequently, low-pass rectangular signal spectra are assumed, and the output signal-to-noise ratios for various delay rates and time-bandwidth products are numerically evaluated. For zero delay rates, the output signal-to-noise ratio is a linear function of the time-bandwidth product, but for nonzero delay rates, optimum points exist.