# Dictionary:Crosscorrelation

A measure of the similarity of two waveforms, of the degree of linear relationship between them, or of the extent to which one is a linear function of the other. For two waveforms and , the normalized crosscorrelation function is given as a function of the time shift ; between the functions by

For digital data this becomes

The denominator in the above two expressions is the **normalizing factor** and is often omitted (as in Wiener filtering). When normalized, a crosscorrelation of 1 indicates a perfect match, values near zero indicate very little correlation, and negative values indicate that one of the wavelets is inverted. Normalized crosscorrelation is also called **correlation coefficient**. See also *autocorrelation*. Nonnormalized crosscorrelation can be accomplished by reversing one function in time and convolving:

The equivalent operation in the frequency domain involves multiplying the amplitudes of common frequencies and subtracting phase-response curves. See Sheriff and Geldart (1995, 287–288 and 541–543).