Properties
- The correlation of functions f(t) and g(t) is equivalent to the convolution of f *(−t) and g(t). I.e.:
- If f is Hermitian, then
- Analogous to the convolution theorem, the cross-correlation satisfies:
where denotes the Fourier transform, and an asterisk again indicates the complex conjugate. Coupled with fast Fourier transform algorithms, this property is often exploited for the efficient numerical computation of cross-correlations. (see circular cross-correlation)
- The cross-correlation is related to the spectral density. (see Wiener–Khinchin theorem)
- The cross correlation of a convolution of f and h with a function g is the convolution of the correlation of f and g with the kernel h:
Read more about this topic: Cross-correlation
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