Reassembling Fourier Transforms
- To: mathgroup at smc.vnet.net
- Subject: [mg48860] Reassembling Fourier Transforms
- From: Lee Fisher <lfis at helix.nih.gov>
- Date: Sat, 19 Jun 2004 04:31:18 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I am trying to turn a list of points into a function, and one of the ways I thought to do this was to use Fourier to find the frequency components of the list, and then to Create a sum of exponentials as follows: f[x_] := Random[NormalDistribution[0, 1]] rawnoise = Table[f[x], {x, 1, 1000}]; frawnoise = Fourier[rawnoise]; magrawnoise = Abs[rawnoise]; phaserawnoise = Arg[frawnoise]; c[t] := \[Sum]\+\(n = 1\)\%1000\(( .005\ magrawnoise[\([n]\)]\ E^\((I\ n\ t\ + phaserawnoise[\([n]\)])\))\);\)\) c[t] = Re[c[t]]; I have two questions concerning this. First, is there an easier way to turn a set of random values into a function so that NDSolve can move through the function and always find the same value at a given point (i.e. c[6] will always equal .6002)? Second, if not, what sort of factors are necessary in adjusting the phase and magnitude so that they match the original numbers. I've tried doing this with much simpler inputs, such as two sine waves (Sin[t]+Sin[2 t]) and still the output does not properly match the input. Thanks for any help, Lee