A common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period. This correspondence analyzes and assesses the pitfalls of this approach. It is shown that this yields a biased estimate of the time delay, with both the bias and variance of the estimate dependent on the location of the delay between samples, SNR, signal and noise bandwidths, and the prefilter or window used in the generalized correlator.
Ahtruct-Under consideration is the effectiveness of various windowing functions in the generalized correlator when a strong spectral peak, i.e., a sinusoid, is present in the signal. The windows W~I I ( W ) and WXOT(W) or &(w) avoid the ambiguity problem that is encountered by the other windows when sinusoids are present in the signal.
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