Slide a signal against a delayed copy of ITSELF and measure how well they match at each delay. At delays equal to the signal’s hidden period, the copy lines up and the match SPIKES — so autocorrelation finds a repeating beat buried in noise, even one you can’t see. It’s how a tuner hears your pitch and how radar finds an echo. Slide the lag and watch the peaks reveal the period.
Autocorrelation measures a signal’s similarity to a time-shifted copy of itself: R(τ)=Σₙ x[n]x[n+τ]. It peaks at τ=0 (perfect self-match) and again at every lag equal to a PERIOD of any repetition — so it extracts periodicity and pitch even when buried in noise (noise, being uncorrelated with itself at nonzero lag, averages away). By the Wiener–Khinchin theorem it is the inverse Fourier transform of the power spectrum, tying it to [[the-fourier-transform]]. Used in pitch detection, radar/sonar ranging, and time-series analysis. A fail-loud self-check throws unless a period-4 signal shows a positive peak at lag 4. ◆ real signal math, node-verified.
Autocorrelation finds periodicity and delay but discards absolute phase; strong harmonics can produce octave errors in pitch tracking. The peak-at-the-period property and Wiener–Khinchin link are exact.