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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)
```

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