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RE: FourierTransform rect func

• To: mathgroup@smc.vnet.net
• Subject: [mg11955] RE: [mg11925] FourierTransform rect func
• From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
• Date: Fri, 10 Apr 1998 01:03:44 -0400

Song Sam Liang  wrote:
|
|  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] |
|
To use the definition of FT that you want you need to use a non-default
for  the FourierFrequencyConstant option.

I don't think the FT command can handle functions defined with  (If) 
 statements.
However, it gives the result you expect when the function is defined
with  the UnitStep function.

In[1]:=
<<Calculus`FourierTransform`

In[7]:=
<<Calculus`DiracDelta`

In[8]:=
rect[x_]:=UnitStep[x+1/2]-UnitStep[x-1/2]

In[9]:=
SetOptions[FourierTransform, FourierFrequencyConstant->-2 Pi];

In[10]:=
FourierTransform[rect[t],t,f]

Out[10]=
Sin[f*Pi]/(f*Pi)

_________________
Ted Ersek