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
- References:
- FourierTransform
- From: chris@tabla15.freeserve.co.uk (Chris Parker)
- FourierTransform