On Thu, May 31, 2012 at 11:14 PM, Mike Miller <mtmil...@ieee.org> wrote:
> On Thu, May 31, 2012 at 4:42 PM, Juan Pablo Carbajal
> <carba...@ifi.uzh.ch> wrote:
>> Hi,
>>
>> I have a question concerning xcorr for the case of vector input.
>>
>> The results of xcorr do not match with the ones suing the straight formula
>> http://en.wikipedia.org/wiki/Autocorrelation#Estimation
>>
>> In particular taking the vector
>> x = rand(4069,1);
>>
>> xcorr with option 'coeff' and 'biased' show a linear trend that the
>> mentioned formula doesn't show. I guess this comes from the fact that
>> the data has nonzero mean value and the formula removes it, while
>> xcorr doesn't.
>>
>> Is this the expected behavior?
>
> Yes. In fact rewind a little bit on the page you cite:
> http://en.wikipedia.org/wiki/Autocorrelation#Signal_processing
>
> In signal processing, the above definition is often used without the
> normalization, that is, without subtracting the mean and dividing by
> the variance. When the autocorrelation function is normalized by
> mean and variance, it is sometimes referred to as the
> autocorrelation coefficient.
>
> "Normalization" here is referring to the data samples, as opposed to
> the "scale" options that xcorr accepts.
>
>> If it is, we should improve the help text to mention this fact explicitly.
>
> I think this is typical of different interpretations of some
> terminology between statistics and signal processing. If you want to
> propose some clarifying text, keep in mind that for signal processing
> oriented users this is naturally the correct behavior. See for
> example "help autocov" in Octave core.
>
> --
> mike
Hi mike,
Thank you! Indeed you are right.
autocov from core is obsolete, however xcov from signal package will
replace it. Indeed xcov follows the statistical definition. We should
add in xcorr
"This function uses the conventions from digital signal processing.
For the statistical conventions see @code{xcov}."
or something like that. I will go to sleep now, but if you haven't
done it by tomorrow I will do it.
Thanks
--
M. Sc. Juan Pablo Carbajal
-----
PhD Student
University of Zürich
http://ailab.ifi.uzh.ch/carbajal/
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