       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

>

```

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