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 >