[PYTHON MATRIX-SIG] autocorrelation functions?

[Konrad Hinsen]

> 1) I can do 2d fft's and 2d inverse fft's -- what kind of
>    autocorrelation metric would that use (meaning if autocorrelation is
>    the function relating distance between elements and their
>    correlation, what distance metric does it use)?

If you apply everything to 2d arrays, you end up with a 2d answer,
meaning a correlation function of two variables, i.e. a distance
*vector*. I suspect that you can get your total correlation by
averaging over all array elements corresponding to a fixed
"distance", whatever its definitions. For cartesian distance
that would mean averaging over "circles" (with the problem that
there will be very few points with exactly the same cartesian
distance), and for city-block distance averaging over pairs
of diagonal-parallels.

But I strongly recommend checking this before believing it!
I spent less than a minute thinking about it ;-)

> 2) I'd really appreciate a reference on these sorts of tidbits --
>    computational algorithms which cross standard boundary distinctions.
>    Can anyone recommend such a book?

Numerical Recipes did a good start, treating FFT together with
"ordinary" numerical algorithms (and it does say something about
convolutions and correlations). In general, the walls between
subfields seem to be too high to permit useful books like this.

Konrad.
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Konrad Hinsen                          | E-Mail: hinsen@ibs.ibs.fr
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