What is correlation and how is it used in signal processing?

Correlation measures similarity between signals. Autocorrelation compares a signal with time-shifted versions of itself, revealing periodicity and power spectral density (via Wiener-Khinchin theorem). Cross-correlation compares two different signals, used for time delay estimation and pattern matching. Mathematical form similar to convolution but without time reversal. Applications: Radar/sonar (range detection), GPS (code synchronization), Speech recognition, Communication (synchronization), and Image matching. Efficient computation via FFT (correlation theorem: correlation in time = conjugate multiplication in frequency).