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MathGroup Archive 2012

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How FFT workks? (analytical example)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127424] How FFT workks? (analytical example)
  • From: juan miguel <juanmixp at gmail.com>
  • Date: Mon, 23 Jul 2012 19:56:32 -0400 (EDT)
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  • Delivered-to: mathgroup-newout@smc.vnet.net
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First of all, thanks for reading my post.
Well, the problem is the next one:

I have to make an Inverse Fast Fourier Transfrom of a function, but I'm not sure how it works. To do this, I have used a function whose Inverse Fourier Transform is analytical

        -G
f(w)= -------
       w+iG/2

So the analytical solution can be easily calculated:

Assuming[G > 0,InverseFourierTransform[f[w], w, t]]

and the solution is:

i Exp(-t G /2)Sqrt(2*pi)G*HeavisideTheta[t]

And now I can Plot this function (the imaginary part)

Well, what I want is to get exactly the same result using the subrutine Fast Fourier Transfrom (InverseFourier) with that function, but I do not know how to this.

It is very important for me, because the function that I have to use has not analytical solution and I have to be sure about what I am doing

Thanks



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