Cross-correlation

In signal processing, cross-correlation or sometimes simply correlation is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time between the signals, is sometimes called the sliding dot product, and has applications in pattern recognition and cryptanalysis.

For discrete functions f _i and g _i the cross correlation is defined as

$(f\star g)_i \equiv \sum_j f^*_j\,g_{i+j}$

where the sum is over the appropriate values of the integer j and an asterisk indicates the complex conjugate. For continuous functions f (x) and g _i the cross correlation is defined as

$(f\star g)(x) \equiv \int f^*(t) g(x+t)\,dt$