Encyclopedia > Autocorrelation

  Article Content

Autocorrelation

Autocorrelation is a mathematical tool used frequently in digital signal processing for analysing series of values, such as time domain signals.

Formally, the autocorrelation R at distance j for signal x(i) is R(j) = E{[x(n)-m]*[x(n-j)-m]}, where the expected value operator E{} is taken over n, and m is the average value (expected value) of x(i). Quite frequently, autocorrelations are calculated for zero-centered signals, that is, for signals with zero mean. The autocorrelation definition then becomes R(j) = E[x(n)*x(n-j)], which is the definition of autocovariance[?].

Multi-dimensional autocorrelation is defined similarly, that is, for example in three dimensions R(j,k,l) = E{[x(n,m,p)-m]*[x(n-j,m-k,p-l)-m]}. In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases.

A fundamental property of the autocorrelation is symmetry, R(i) = R(-i), which is easy to prove from the definition.

This needs a lot more work...



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Dennis Gabor

...     Contents Dennis Gabor Dennis Gabor (Gábor Dénes) (1900-1979) was a Hungarian physicist. He invented holography in 1947, for ...

 
 
 
This page was created in 46.6 ms