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MathGroup Archive 2000

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Re: Incorrect Fourier Transorms?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24834] Re: Incorrect Fourier Transorms?
  • From: "Kevin J. McCann" <Kevin.McCann at jhuapl.edu>
  • Date: Tue, 15 Aug 2000 03:04:05 -0400 (EDT)
  • Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
  • References: <8n5j1q$n24@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I get the same results you did, including the correct answers with the
default. Looks like a "feature" to me.

Kevin

<iliketrash at aol.com> wrote in message news:8n5j1q$n24 at smc.vnet.net...
>
> Hi All:
>
> In using the symbolic Fourier transform feature of Version 4,
> specifically, FourierTransform and InverseFourierTransform, it seems
> easy to obtain incorrect results. One would expect the following two
> cells to give identical results, but they do not. The first cell
> correctly returns the original time function after the two transforms,
> but the second cell results in a time-reversed version of the original
> time function. The result seems to depend upon when a value is assigned
> to the exponential part of the time function.
>
> The same sort of thing happens when using FourierParameters -> {0, -2
> Pi}. However, using the default values of FourierParameters, or {-1, 1},
> doesn't appear to cause problems.
>
> Does anyone else have this problem or am I misusing these functions?
>
> Incidentally, the first cell returns a time function (after double
> transformation) that, although correct, is quite far from being fully
> simplified; the second cell returns a concise, (although incorrect)
> function.
>
>
>
> In[121]:=
> Clear[b];
> FourierTransform[UnitStep[t]*Exp[-b t], t, w,
>     FourierParameters -> {1, -1}]
> InverseFourierTransform[%, w, t, FourierParameters -> {1, -1}]
> b = 2;
> Plot[%%, {t, -3, 3}, PlotRange -> All]
>
>
> In[126]:=
> a = 2;
> FourierTransform[UnitStep[t]*Exp[-a t], t, w,
>     FourierParameters -> {1, -1}]
> InverseFourierTransform[%, w, t, FourierParameters -> {1, -1}]
> Plot[%, {t, -3, 3}, PlotRange -> All]
>
>
>
> Jerry
>




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