Re: Confused about correlations in sequence of Random[] numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg73057] Re: Confused about correlations in sequence of Random[] numbers
- From: dh <dh at metrohm.ch>
- Date: Wed, 31 Jan 2007 00:40:49 -0500 (EST)
- References: <epnaca$d3u$1@smc.vnet.net>
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
>