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MathGroup Archive 2002

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Re: FourierTransform problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35118] Re: FourierTransform problem
  • From: wempenj at asme.org (JDW)
  • Date: Tue, 25 Jun 2002 03:42:31 -0400 (EDT)
  • References: <af6hts$ll4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

David Turner <dturner at faulkner.edu> wrote in message news:<af6hts$ll4$1 at smc.vnet.net>...
> Hello,
> 
> I am using Mathematica for Students 3.0.1 with Windows 98.  When I execute
> the following code, I get the error messages below:
> 
> In[1]:=
> <<Calculus`FourierTransform`
> 
> In[2]:=
> Clear[fx, fw, a]
> 
> In[3]:=
> a:=1
> 
> In[4]:=
> fx[x_]:=Exp[-Abs[x*a]]
> 
> In[5]:=
> fw[w_]:=InverseFourierTransform[fx[x], x, w]
> 
> In[6]:=
> Plot[fw[w], {w, -5*a,5*a}]
> 
> Plot::plnr : fw[w] is not a machine-size real number at w = -5..
> Plot::plnr : fw[w] is not a machine-size real number at w = -4.59433..
> Plot::plnr : fw[w] is not a machine-size real number at w = -4.15191..
> General:: stop : Further output of Plot::plnr will be suppressed during this
> calculation.
> 
> Does anyone know where I might obtain a corrected FourierTransform.m package
> for Mathematica 3.0.1?  My copy is dated 7/21/97.  I contacted Wolfram about
> this matter.  However, they told me they no longer support version 3.0.  I
> appreciate any help you may provide.
> 
> Thanks.
> 
> David

David,

The problem doed not exist in the FourierTransform package but in your
function deffinition. You have used the SetDelayed operator (:=) to
define all your fuctions. This holdes the function unevaluated and is
evaluated afresh each time it is called. You have several options to
fix this.

Evlauate fx[x] in the fw[w] function (very slow for plotting the
function fx[x] must me evlauted afresh for each point the the plot)

fw[w_] := InverseFourierTransform[Evaluate[fx[x]], x, w]

or you may evlautate the fw[w] function in the plot command (slightly
faster)

Plot[Evaluate[fw[w]], {w, -5*a, 5*a}] 

or best yet don't use the := operator when you don't need to.

Needs["Calculus`FourierTransform`"]
Clear[fx, fw, a] 
a = 1;
fx[x_] = Exp[-Abs[x*a]];
fw[w_] = InverseFourierTransform[fx[x], x, w];
Plot[fw[w], {w, -5*a, 5*a}]

Also you can avoid shadowing problems (they can be quite confusing) by
using the Needs[] function to read in packages rather than <<.

--JDW


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