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FourierTransform rect function

• To: mathgroup@smc.vnet.net
• Subject: [mg11925] FourierTransform rect function
• From: Song Sam Liang <sliang1@leland.Stanford.EDU>
• Date: Thu, 9 Apr 1998 00:33:26 -0400
• Organization: Stanford University

Hi.,

  I am having trouble with doing Fourier Transform on user-defined
functions.  In particular, I can't transform a rect function.  The
transcript is as follows:

In[1]:= rect[x_] = If[Abs[x]>1/2, 0, 1] Out[1]= If[Abs[x] > 1/2, 0, 1]

In[2] := FourierTransform[rect[t], t, f] Out[2]=
FourierTransform[If[Abs[t]>1/2, 0, 1], t, f] # It refuses to do F.T
here

However, I can manually do the F.T:
In[3] := Integrate[rect[t] Exp[-I 2 Pi f t], {t, -Infinity, Infinity}]
Out[3] = (Exp[-I f Pi] - Exp[I f Pi) I / (2 f Pi)

In[4] := ExpToTrig[%]
Out[4] = Sin[f Pi] / (f Pi)

This is correct F.T.

  Does anybody know where I did wrong here?  Thank your for your help in
advance.

Sam

-- 
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Song Sam Liang
Graduate Student, Department of Electrical Engineering, Stanford
University
sam.liang@stanford.edu, song.liang@stanford.edu (650) 725-7062 (W),
(650) 497-6491(H)
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