What is Autocorrelation Time & Covariance?

[jophysics]

Hi everybody, please someone can explain me what is the autocorrelation time and how it is linked to coviarance?

thank you!

 

[Andy Resnick]

In signal processing, the autocorrelation time can mean the time it takes for a signal to 'lose it's memory'. For example, plotting the position of a diffusing particle over time and autocorrelating the signal gives a short-time scale where the position is non-random as compared to previous positions, and a longer time scale where the current position is not correlated with earlier positions. Autocorrelation is used a lot in light scattering experiments as well- it gives a scale for the dynamics of the system. Also in optical processing techniques such pattern recognition.

Covariance is a more general way of discussing the coherence properties of *two* signals, but probably reduces to the autocorrelation when the signals are from the same source.

 

[atyy]

Covariance is the correlation of the deviation from the mean.

It is the same as the correlation if the mean(s) of the analyzed signal(s) is/are zero.