In signal processing, autocorrelation is a mathematical tool used to measure the similarity of a signal with itself at different points in time. It is defined as the correlation between a signal and a time-shifted version of itself. In the case of real signals: $ R_{x x}(m) = \sum_{n=-\infty}^{+\infty} x(n) x(n+m) $ The above equation can be expressed in terms of the [[convolution sum]]: $ R_{x x}(n) = \sum_{l=-\infty}^{+\infty} x(l)x(-(n-l)) = x(n) \ast x(-n) $ The autocorrelation can be used to find periodic components concealed in noise. For example: ![[Acf_new.svg|400]] [Wikimedia](https://commons.wikimedia.org/wiki/File:Acf_new.svg The autocorrelation can be used to assess the presence of a periodic component in a non-periodic and to estimate its [[fundamental frequency]], for example in a voiced [[fricative consonant]] such as \[v\].