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
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]
Applications
  • 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.

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Subjects: Noise & Vibration Signal Processing