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Re: exponent_decay_of_fourier_fransform_of_brownian_motion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41924] Re: exponent_decay_of_fourier_fransform_of_brownian_motion
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 10 Jun 2003 04:46:55 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <bbq6sl$cva$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

1/f is perfect for Brown noise. What's your problem ?

Regards
  Jens

"Jose R. Campanha" wrote:
> 
> Dear mathgroup
> 
> I'd like to find the value of the exponent decay of the fourier
> transform of the brownian motion
> (that I think is near 2), then I do
> 
> <<Statistics`ContinuousDistributions`
> <<Graphics`Graphics`
> 
> ndist = NormalDistribution[0, 1]
> 
> RandomWalk[n_]:=Flatten[NestList[#+RandomArray[ndist,1]&,0,n]]
> 
> list1=RandomWalk[4096];
> 
> ListPlot[list1,PlotJoined->True]
> 
> list2=Chop[Abs[Fourier[list1]]];
> 
> LogListPlot[list2,PlotJoined=True,PlotRange=All]
> 
> list3=Drop[list2,-2049];
> 
> Length[list3]
> 
> len=Length[list3]
> 
> freq=0.5 Range[len]/len;
> 
> Length[freq]
> 
> power=list3;
> 
> endlist=Transpose[{freq,power}];
> 
> LogListPlot[endlist,PlotJoined=True,PlotRange=All];
> 
> Fit[Log[endlist],{1,x},x]
> 
> And the value was near 1.
> 
> Could someone help?
> 
> Jos=E9 R. Campanha
> 
> Physics Dpto
> 
> UNESP - Rio Claro


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