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RE: Confused about correlations in sequence of Random[] numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg73060] RE: [mg73037] Confused about correlations in sequence of Random[] numbers
• From: "Owen, HL \(Hywel\)" <h.l.owen at dl.ac.uk>
• Date: Wed, 31 Jan 2007 00:52:52 -0500 (EST)

Thanks! I worked that out myself earlier on, but it's good to have it
confirmed by someone else.

The easy way to think about it is in this table for shifts of 2:

x1 x2 x3 x4 x5 x6
x3 x4 x5 x6 x1 x2
x5 x6 x1 x2 x3 x4

So that the sums of, say, columns 1, 3 and 5 are all the same. Hence the
strong component at wavelength = 2.

Doh! Should have been obvious to me.

Hywel 

> -----Original Message-----
> From: dh [mailto:dh at metrohm.ch] 
> Sent: 30 January 2007 12:10
> To: Owen, HL (Hywel)
> Subject: Re: Confused about correlations in sequence of 
> Random[] numbers
> 
> Hi Owen,
> correlation tells you how much you have to "shift" a kernel 
> function that it fits "well" a trial function.
> Now, if you have a sum of shifted functions, the function 
> itself will fit "best" if you shift it be one of the shifts 
> contained in the sum.
> Daniel
> 
> Owen, HL (Hywel) wrote:
> > Hi folks,
> > 
> > I'm confused about what this all means.
> > 
> > First, I make a list of Uniformly-distributed random 
> numbers. Then I 
> > make copies of this list rotated by n,2n,3n,4n... and I 
> make m copies. 
> > I then add the numbers together, and look at these values and their 
> > Fourier transform. The whole thing is done like this:
> > 
> > list1 = Table[Random[], {1000}];
> > lists = Table[RotateLeft[list1, 8n], {n, 1, 20}]; olist = Plus @@ 
> > lists; ListPlot[olist, PlotJoined -> True]; 
> > ListPlot[Re[Fourier[olist]], PlotJoined -> True, AxesOrigin -> {0, 
> > 0}];
> > 
> > I see very strong correlations, but I don't understand why. 
> Can anyone 
> > give me a simple explanation? I'm sure there is one, but I 
> don't see it.
> > 
> > Hywel
> > 
> 
>