Incorrect Fourier Transorms?

• To: mathgroup at smc.vnet.net
• Subject: [mg24813] Incorrect Fourier Transorms?
• From: iliketrash at aol.com
• Date: Sun, 13 Aug 2000 03:16:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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