Correlation Theory

In probability theory and statistics, correlation indicates the strength and direction of a linear relationship between two random variables. In signal processing, the cross-correlation is a measure of the similarity of two signals and autocorrelation is the correlation of a signal with itself. For time domain signals, autocorrelation corresponds to the strength of a relationship as a function of the time separation between them.

Fig. 1 depicts correlation of a time domain signal with itself.

Fig. 1 Time Domain Signal Autocorrelation

Fig. 2 depicts the correlation function corresponding to the signal autocorrelation of Fig. 1.

Fig. 2 Correlation Function

For magnet field structures, autocorrelation corresponds to the strength of a relationship as a function of the spatial separation between them.

Complementary autocorrelation is the correlation of a magnetic field structure with its mirror image (see Fig. 3).

Fig.3 Complementary Autocorrelation

Anti-complementary autocorrelation is the correlation of the equal faces of two complementary magnetic field structures (see Fig. 4).

Fig.4 Anti-complementary Autocorrelation