# Autocorrelation

- The autocorrelation function gives a measure of the extent to which a signal correlates with a displaced version of itself, as a function of the displacement.
- where
*R*_{AA}(τ) = autocorrelation of signal A as a function of displacement*f*_{A}= signal A as a function of time*(t)*= length of signal over which each correlation is calculated [s]*T*- τ = displacement time [s]

- Detection of echoes in a signal and measurement of their strength and associated time delays.
- The detection of periodicity buried in noise, since the autocorrelation of a periodic signal is also periodic whereas that of noise (a random signal) falls rapidly to zero with increasing time displacement.

**Applications**

**See also: **Autocovariance, Cepstrum, Correlation, Cross Correlation.

**Subjects: ** Noise & Vibration Signal Processing