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 > > > >