Re: autocorrelation

[Ted Harding]

( 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)