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.
- RAA(τ) = autocorrelation of signal A as a function of displacement
- fA(t) = signal A as a function of time
- T = length of signal over which each correlation is calculated [s]
- 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.
See also: Autocovariance, Cepstrum, Correlation, Cross Correlation.
Subjects: Noise & Vibration Signal Processing