Applications of Correlation in Signal Processing There have been discussions on the differences between convolution and correlation, autocorrelation, cross-correlation, et al.


In spite of looking at the visualizations, and understanding the formula for calculation of convolution and correlation, I don't understand the need for correlation - is it required for identifying a signal uniquely?
What is the distinction between correlation and cross-correlation (if any exists)?


I get that convolution can be important in determining system responses to any arbitrary input signals when the impulse response is known, but what are the practical scenarios where correlation is helpful?

I know the theoretical differences between the concepts and this link isn't helpful for my question.
A relatively simple application where correlation is used is in determining timing of a communications signal.  A known synchronization signal will be sent periodically so that the receiver can use it as a point of reference.  How does the receiver use it as a point of reference?  It correlates the incoming signal stream against the known sequence, and when the correlation peak is above a certain threshold, it will use the peak to establish symbol timing and make decisions on the symbols to extract a binary sequence.

Correlation usually means cross-correlation, but I think the latter term only exists to be distinguished from auto-correlation.