Re: FourierTransform

• To: mathgroup at smc.vnet.net
• Subject: [mg20617] Re: [mg20602] FourierTransform
• From: "Wolf, Hartmut" <hwolf at debis.com>
• Date: Thu, 4 Nov 1999 02:13:31 -0500
• Organization: debis Systemhaus
• References: <199911020735.CAA26988@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

```Chris Parker schrieb:
>
> I am trying to plot the FourierTransform of the Sin function.
> I know you should get two DiracDelta Functions, and can plot these
> with the signal processing package (SigProc), using SignalPlot[] or
> PeicewisePlot[].
>
> However, When I enter the line
>
> FourierTransform[Sin[x], x, w, FourierParameters -> {1, 1}]
>
> I get the result
>
> I \[Pi] "Delta"[-1 + w] - \I \[Pi] "Delta"[1 + w]
>
> Which I cannot plot unless I remove the complex I

Yes, Chris, that's right. However, even if you define

s = -I*FourierTransform[Sin[x], x, w,
FourierParameters -> {1, 1}]

you can Plot, but won't see anything.

Beware now for the inverse you'll get

In[]:= FourierTransform[s, w, x,
FourierParameters -> {-1, -1}]//Expand//ExpToTrig

Out[]= -\[ImaginaryI] Sin[x]

But if you wan't to see something, e.g. you can do

With[{b = 30},
Block[{DiracDelta = b/Sqrt[Pi]  Exp[-(b#)^2 ] &},
Plot[Evaluate[-I FourierTransform[Sin[x], x, w,
FourierParameters -> {1, 1}]], {w, -2, 2}, PlotRange ->
All]]]

Or

With[{b = 30},
Block[{DiracDelta = b/Sqrt[Pi]  Exp[-(b#)^2 ] &},
Plot[Evaluate[
FourierTransform[Cos[x], x, w,
FourierParameters -> {1, 1}]], {w, -2, 2}, PlotRange -> All]]]

if you remind, what you are doing.

Kind regards, Hartmut

```

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