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Correlation: cross-correlation and autocorrelation

Correlation determines the degree of similarity between two signals. If the signals are identical, then the correlation coefficient is 1; if they are totally different, the correlation coefficient is 0, and if they are identical except that the phase is shifted by exactly tex2html_wrap_inline35703 (i.e. mirrored), then the correlation coefficient is -1.

When two independent signals are compared, the procedure is known as cross-correlation, and when the same signal is compared to phase shifted copies of itself, the procedure is known as autocorrelation.

A function which is related to the correlation function, but arithmetically less complex, is the average magnitude difference function.

Cross-correlation is the method which basically underlies implementations of the Fourier transformation: signals of varying frequency and phase are correlated with the input signal, and the degree of correlation in terms of frequency and phase represents the frequency and phase spectrums of the input signal.

Autocorrelation is a method which is frequently used for the extraction of fundamental frequency, tex2html_wrap_inline35691 : if a copy of the signal is shifted in phase, the distance between correlation peaks is taken to be the fundamental period of the signal (directly related to the fundamental frequency). The method may be combined with the simple smoothing operations of peak and centre clipping, or with other low-pass filter operations.



Dafydd Gibbon
Wed May 22 08:36:40 MET DST 1996