# Autocorrelation & Cross-Correlation -> Main uses in DSP??

It seems this is strongly linked to calculating phase offsets, frequency offset for carrier recovery, symbol timing errors, recovery algorithms, what else?

• Biased version can give difference in constant phase offset between two signals, useful to rotate one set of symbols back into place.
• Biased version can give The difference in power between the two which is useful if I want to get them to the same amplitude.

• I think that the magnitude or absolute of unbiased and unnormalised with no frequency offset or error can give me the bandwidth or Symbol rate of the signal on the Y axis where there is the maximum spike.
• The frequency offset can be obtained from the imaginary part of the autocorrelation, how this is implemented to correct the offset in carrier recovery is still alluding me.
• For the autocorrelation, this post gives some answers.
– Peter K.
Commented May 30, 2022 at 16:24
• As you learn the details, keep the big picture in mind: correlation is a measure of the similarity between two signals.
– MBaz
Commented May 30, 2022 at 16:30
• Oh yeah. Matched filters. Also for binary or M-ary communication (which is really your first example). You have a constellation of signals all associated with a message containing some bits (the simplest is, of course, binary which is a constellation of two given signals, one for a 0 and another for 1. But you could have a constellation of 16 signals in a 4 $\times$ 4 grid or something like that. I think we call those "symbols" or similar. Given a noisy received signal you cross-correlate each symbol in the constellation and see which one the received signal resonates best with. Commented Jun 26, 2022 at 18:09