Keresztkorreláció

Keresztkorreláció is a statistical measure that quantifies the similarity between two series of data as a function of the displacement of one relative to the other. In simpler terms, it indicates how well one signal matches another when one is shifted. The cross-correlation function is computed by calculating the integral of the product of two functions, where one function is reversed and shifted. For discrete signals, this becomes a summation.

The resulting cross-correlation value at a specific lag (shift) indicates the degree of similarity between the two signals at that particular displacement. A high positive correlation at a certain lag suggests that the signals are similar and aligned when one is shifted by that amount. A high negative correlation indicates that the signals are similar but out of phase. A value close to zero suggests little to no linear relationship at that lag.

Keresztkorreláció has wide-ranging applications. In signal processing, it's used for tasks like pattern recognition, echo detection, and estimating time delays. In image processing, it can be employed for template matching or object detection. It also finds use in econometrics to analyze relationships between economic time series and in neuroscience to study the synchrony of neural activity. The concept is fundamental to understanding how signals or data sets relate to each other over time or space.