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## Re: autocorrelation

**From**: |
Ted Harding |

**Subject**: |
Re: autocorrelation |

**Date**: |
Thu, 27 Apr 1995 16:30:48 +0200 (BST) |

( Re Message From: Francesco Potorti` )
>* *
>* I need to compute the autocorrelation of vectors. I started with the*
>* following experiment:*
>* *
>* kk=[2,3,4,5]*
>* kk =*
>* *
>* 2 3 4 5*
>* *
>* fftconv(kk,kk)*
>* ans =*
>* *
>* 4 12 25 44 46 40 25*
>* *
>* I would have expected *
>* *
>* 10 23 38 54 38 23 10*
>* *
>* instead. What am I doing wrong?*
There's nothing wrong with the answer from fftconv. This computes
a CONVOLUTION, which is defined as
Sum[over s] x(s) * x(t-s)
i.e. one of the factors is taken in the reverse order.
The CORRELATION [at lag t = -(N-1), .. 2, 1, 0, 1, 2, .. , (N-1)]
which you want is defined by
Sum[over s] x(s) * x(s-t) = R(t) = R(-t)
You can get it the right way roud by reversing one of the arguments
to fftconv, if you wish. This gives the result you expected.
Ted. (address@hidden)

**autocorrelation**, *Francesco Potorti`*, `1995/04/27`
**Re: autocorrelation**,
*Ted Harding* **<=**