autocorrelációs

Autocorrelation is a mathematical tool used to measure the similarity between a signal and a delayed version of itself as a function of the delay. It is essentially a correlation of a signal with itself. The autocorrelation function, denoted as R(τ), quantifies how much a signal resembles a shifted version of itself. A high value of R(τ) for a specific delay τ indicates a strong similarity at that offset, suggesting a repeating pattern or periodicity in the signal. Conversely, a low value indicates little similarity.

The concept of autocorrelation is widely applied in various fields. In signal processing, it is used to identify periodicities, determine the fundamental frequency of a signal, and in noise reduction techniques. In statistics, it helps in understanding the dependence between observations in a time series, crucial for forecasting and modeling. Econometrics uses autocorrelation to analyze time-dependent data like stock prices or economic indicators. In image processing, it can be used for texture analysis and pattern recognition. The calculation typically involves integrating the product of the signal and its time-shifted replica over a certain period. Discrete signals are handled using summation instead of integration.