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Is there a built in function to compute the autocorrelation of a signal ?

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You can get ListCorrelate to do this. – Szabolcs Feb 23 '12 at 14:17

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up vote 7 down vote accepted

From the help file for ListConvolve, to find the autocorrelation of a list:

data = Table[Mod[i^2, 17], {i, 100}];
autocorrelation = ListConvolve[data, data, {1, 1}];
ListLinePlot[autocorrelation ]

Mathematica graphics

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This only works because the list in the example is circularly even. (# == Reverse[#]) &@Rest@Table[Mod[i^2, 17], {i, 100}] gives True – Rojo Feb 23 '12 at 14:22
up vote 1 down vote

If you search the docs for "autocorrelation", ListConvolve turns up. There's also ListCorrelate. Does this work for you?

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@Rojo the point I was sort of making is that typing "autocorrelate" in the help viewer takes you to ListConvolve which has an example. – acl Feb 23 '12 at 14:21
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Perhaps this satisfies you?

autocorrelate[exp_, varFrom_, varTo_]:=Convolve[exp, exp/.varFrom->-varFrom, varFrom, varTo]

If your signal is discrete but symbolic, change Convolve to DiscreteConvolve. If they are lists, check out ListCorrelate

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up vote 8 down vote

Yes, in version 9 you have CorrelationFunction built in.

data = Table[Mod[i^2, 17], {i, 100}];
autocorrelation = CorrelationFunction[data, {0, Length[data] - 1}];

ListLinePlot[autocorrelation]

autocorrelation

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@OleksandrR Thanks, I missed this in the documentation! (It's also ~100 faster :) – Ajasja Feb 21 at 14:16

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