In signal analysis , the cross-correlation function is used to describe the correlation between two signals and when there are different time shifts between the two signals. Cross stands for the case of the function:
If it is a weakly stationary process , the correlation function is no longer on the choice of the times is and , but only on their difference dependent.
Analogously, the discrete cross-correlation, which plays an essential role in the field of discrete signal processing, with the sequence and a shift is defined as:
= (Energy signals)
= (Power signals)
In digital signal processing, on the other hand, finite averaging with arguments starting at index 0 is required due to the architecture of computer registers, of which there is a pre-stressed and a non-pre-stressed version:
She shows z. B. peaks in time shifts that correspond to the signal transit time from the measurement location of the signal to the measurement location of the signal . Differences in transit time from a signal source to both measurement locations can also be determined in this way. The cross-correlation function is therefore particularly suitable for determining transmission paths and locating sources.
Is one of the signals or zero symmetrical, i. H. their mean value over the signal is zero or , the cross-correlation is identical to the cross-covariance. Well-known representatives of the zero-symmetric functions are, for example, the sine and cosine functions.
Bernd Girod, Rudolf Rabenstein, Alexander Stenger: Introduction to systems theory . 4th edition. Teubner, Wiesbaden 2007, ISBN 978-3-8351-0176-0 .