Extraction of Linearly Ranging Signals with a Scanning Correlator
D. H. Tack, R.E. Ziemer, Robert F. Lambert · The Journal of the Acoustical Society of America · 1963
When a correlation receiver is used to extract signals emanating from moving sources from additive noise backgrounds, a time-varying correlation function results. An extension of the analysis of Davenport, Johnson, and Middleton [J. Appl. Phys. 23, 377–388 (1952)] for correlators with fixed delay and finite averaging time is made to the case of linearly time-varying delays to enable the calculation of the mean and variance of the output as a function of observation time. It is shown, in the case of a scanning correlator, that proper choice of the scan rate k minimizes the error in the extraction of the correlation function of the ranging signal. Some experimental measurements of the output mean of a scanning correlator are presented and compared with theoretical results. The output variance of the correlator also is discussed. In the case of coherent extraction, the variance can be shown to be of the form of the product of the variances of the input noise and signal divided by a Nyquist sample size. This Nyquist sample size is given by 2WSN Ta, where WSN is the noise-equivalent bandwidth of the spectrum formed by the convolution of the signal and noise spectra and Ta is an equivalent integration time of the averaging filter. [This research was supported by grants from the National Science Foundation.]