Cross-correlation

In the signal analysis, the cross-correlation function is used to describe the correlation of two signals, at different time shifts between the two signals. The following applies:

In shorthand notation the operator symbol is used for the cross-correlation:

With than the complex conjugate of. The cross-correlation convolution operation is identical to the illustrated through the following relation by the convolution operator:

Similarly, the discrete cross-correlation, this plays in the field of digital signal processing, an essential role defined with the result and a shift as:

Properties

And

As well as

With the autocorrelation functions and and the observed time window length.

The function is neither even nor odd. It shows, for example, peaks at time offsets corresponding to the signal propagation time of the signal from the measuring location to the measurement location of the signal. Also, run-time differences from a signal source to two monitoring sites can be detected in this way. The cross correlation function is therefore particularly suitable for the determination of pathways and locating sources.

Technically computing the cross-correlation function is usually determined via the inverse Fourier transform of the cross-power spectrum: