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