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MathGroup Archive 1994

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Re: Autocorrelation and Random Numbers

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Autocorrelation and Random Numbers
  • From: Richard L. Bowman <r.l.bowman at cescc.bridgewater.edu>
  • Date: 09 Mar 94 07:59:02 EST

Thanks to those who sent me private mail with help on how to correct my
formula for autocorrelation.  The problem was one of normalization.  I'm
still not sure of the correct reason for the situation, but I did find
a solution.

I calculate the autocorrelation as before;
 In[5]:=
     correl = Chop[
        InverseFourier[Fourier[ran] Conjugate[Fourier[ran]]]]
Than I take the first value and divide all terms in the list by this 
number.  This way the first term becomes 1.00000 as it should be 
(there is a "perfect" correlation between a list and itself!)

I checked my modified values by generating code in Mma to actually
calculate the autocorrelation vector by "hand".  The two vectors
compare exactly, but the Fourier Transform method is obviously much
faster.
-----------------------------------------------------------------------
    Richard L. Bowman
    Dept. of Physics, Bridgewater College, Bridgewater, VA  22812
    <r.l.bowman at bridgewater.edu>                     703-828-2501
-----------------------------------------------------------------------





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