# Physical meaning of autocorrelation

1. Jan 9, 2013

### jollage

Hi All,

I was in a process of processing my vibration-test data. I now generated a plot of the autocorrelation function of the object acceleration. Please see the attachements (the second attachment is the close-up for small tau's).

The x-axis in the plot is the time delay tau. You can see from the second attachment that, at tau=0,the autocorrelation reaches its maximum.

My question is, as for the signal like this, in the long time delay (tau=60s, 70s), the autocorrelation still does not decay too much. What could this behavior imply? In terms of the noise frequency, what can we say?

Mz

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Last edited: Jan 9, 2013
2. Jan 9, 2013

### Jano L.

The autocorrelation function gives the amount of correlation of values of the original function at times delayed by $\tau$. If the autocorrelation function vanishes quickly, it means that the value of the function at some time cannot be predicted with success from neighboring values.

If it does not vanish quickly, it means that the behavior of the function is less random; from the value at time 0 one can estimate possible values at future times with better success. For example, if the function is periodic, after one wave one can make reasonable estimate what the next values will be, and the autocorrelation function comes out also periodic. But if the function is position of Brownian particle, the next values are hard to predict successfully, and also the autocorrelation function decays very fast (exponentially).

3. Jan 9, 2013

### sophiecentaur

If the autocorrelation does not die away then there must be some significant periodic elements in the signalbecause the delayed signal correlates well with an earlier version of itself.

4. Jan 9, 2013