Dude, Look back and smile at what used to happen.

PDP11 & LSI11's and well, VMS are well worth reminiscing about. As are sonars of yesteryear.

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BTW: What some fields call auto-correlation, others call cross-correlation, also no uniformity of correlation, versus correlation coefficient, while most seem to agree on covariance. All have the same concepts, just shift the boundaries of the names round.

For some, autocorrelation has a shift and cross measn between two signals. For others, if the offset is not zero, they call it cross correlation.

If you are a digital guy, the descrete time version of correltaion might be easier to grasp: no integerals; just a summation.

This one includes it.

https://www.allaboutcircuits.com/technical-articles/understanding-correlation/
It also has a section

**Case 2: Identifying Signal Delays**
If you like the stats way: Correlation is a second-order statistic. multiply things together while scanning over time, accumulate. It is a similarity measure. It's not the only one, but it's second order, simple.

If you normalise for power, then a bigger peak means more similar.

If you try if with a repetitive waveform, of course it will be periodic, it's also similar with itself later again. For random signals, with a reasonable bandwidth, not so much of a problem.

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From another angle: The autocorrelation is the Fourier transform of the power spectral density. The cross correlation is the Fourier transform of the cross-spectral density. So the bandwidth of the signals affects the result you get from a correlation. As I said, though, power aside, or normalised by power, a peak means more similar.

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In digital, doing this in the frequency domain can often get you a better answer than directly in time. Taking the Fourier spectrum, multiplying together to generate the cross-spectrum and then an inverse Fourier, can get you sub-sample resolution of the time delay.

https://www.dsprelated.com/showarticle/26.php
Has some of it.

Enjoy.