Re: Fourier Transform Spectroscopy w/ Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg46771] Re: [mg46744] Fourier Transform Spectroscopy w/ Mathematica
• From: Yasvir Tesiram <yat at omrf.ouhsc.edu>
• Date: Sun, 7 Mar 2004 01:33:51 -0500 (EST)
• References: <200403050646.BAA05045@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```G'day,

Stuff like this maybe?
I haven't related the number of points in x to the frequency or
anything and I leave that up to you. Sampling schemes differ between
disciplines and can mean very different things in reality.

Some decaying sinusoid.

fid1 = Table[Cos[20.0t] Exp[-0.10t], {t, 0.0, 10, 0.1}];
l1 = Length[fid1];
ListPlot[fid1, PlotJoined -> True]

Here is the Fourier transform without zero-filling.

ft1 = Fourier[fid1];
left = Take[Re[ft1], (l1 - 1)/2];
right = Take[Im[ft1], (l1 - 1)/2];
(*a phasing step *)
p[a_, b_, im_, re_] := Table[Sin[a + im]] + Table[Cos[b + re]]
ListPlot[p[0, 3.52, left, right], PlotRange -> All, PlotJoined -> True]

Here is the Fourier transform with zero filling. I suppose you now need
a window function having truncated the data somewhat.

l2 = Length[fid2];
ListPlot[fid2, PlotJoined -> True, PlotRange -> All]

ft2 = Fourier[fid2];
left1 = Take[Re[ft2], (l2)/2];
right1 = Take[Im[ft2], (l2)/2];
p[a_, b_, im_, re_] := Table[Sin[a + im]] + Table[Cos[b + re]]
ListPlot[p[0, 3.14, left1, right1], PlotRange -> All, PlotJoined ->
True, Frame -> True]

Yas

On Mar 5, 2004, at 12:46 AM, Kevin Gross wrote:

> Does anybody have an example notebook for transforming interferograms
> into spectra via FFT?
>
> Thanks,
>
> Kevin
>

```

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