lautocorrélation

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 Rxx(τ), describes how the signal's value at a specific time relates to its value at a later time, where τ represents the time lag. A high autocorrelation value at a particular lag indicates that the signal is very similar to its shifted version, suggesting a repeating pattern or periodicity. Conversely, a low autocorrelation value implies little similarity.

The concept of autocorrelation is fundamental in various fields. In signal processing, it is used to identify periodicities within a signal, such as in audio analysis to detect musical notes or in engineering to analyze vibrations. In statistics, autocorrelation is crucial for understanding time series data, helping to determine if past values influence future values. For instance, in economics, it can reveal trends in stock prices or economic indicators. The calculation involves multiplying the signal by a time-shifted version of itself and integrating over all possible shifts. For discrete signals, this becomes a summation. The autocorrelation function is always symmetric around zero lag, and its maximum value occurs at zero lag, where the signal is perfectly correlated with itself.