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MathGroup Archive 2003

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Re: FourierTransform of Sinc Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44429] Re: FourierTransform of Sinc Function
  • From: Bill Rowe <readnewscix at mail.earthlink.net>
  • Date: Sat, 8 Nov 2003 04:51:09 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/7/03 at 5:16 AM, Sorasak at brown.edu (Kieng) wrote:

> I am sorry my question is apparently not so clear.
> I generated a list of data from a sinc function.  I am not doing the
> transform from the sinc function.
> If I use Fourier[list of the data], and plot the result, her is where I am
> kind of not sure why I don't get a top hat function, even though I used very
> fine step for my sinc function data.

There are two issues. First, is the issue of the order of the terms Mathematica returns for the discrete fourier transform. The DC term is first. What you probably want to do is

ListPlot[Flatten@{Take[f, -n/2], Take[f, n/2]}];

where f = Abs[Fourier@data] and n = Length@data

The second issue is the discrete fourier transform returned by Fourier isn't the same as a continuous fourier transform. Basically, when you use Fourier to transform a sampled function, you are taking the transform of a convolution between your function and the comb function. Or in other words, the discrete fourier transform of a discretely sample function isn't the same as a continous fourier transform of the same function.
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