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MathGroup Archive 2007

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Re: Re: FFT of the piecewise step function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77888] Re: [mg77794] Re: FFT of the piecewise step function
  • From: "Peng Yu" <pengyu.ut at gmail.com>
  • Date: Tue, 19 Jun 2007 06:36:07 -0400 (EDT)
  • References: <200706170959.FAA01403@smc.vnet.net>

On 6/17/07, Bill Rowe <readnewsciv at sbcglobal.net> wrote:
> On 6/16/07 at 3:32 AM, pengyu.ut at gmail.com (Peng Yu) wrote:
>
> >mask[x_] := UnitStep[-(x - 1/2)(x + 1/2)(x - 3/2)(x + 3/2)]
> >freq[=C3=B9_]:= FourierTransform[mask[t], t, =C3=B9]
>
> >The solution of freq includes several DiracDelta functions, which
> >should cancel out.
>
> >I'm wondering if there is anyway to make mathematica cancel them
> >out.
>
> You didn't say what version of Mathematica you are using. In
> version 6, I get the following:
>
> In[6]:= m = UnitStep[-(x - 1/2) (x + 1/2) (x - 3/2) (x + 3/2)];
> =46ourierTransform[m, x, w]
>
> Out[7]= (Sqrt[2/Pi]*(Sin[(3*w)/2] - Sin[w/2]))/w
>
> In[8]:= $Version
>
> Out[8]= 6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)
>
> If you are not getting this, you might try using Simplify or FullSimplify


I'm using this version. Even FullSimplify won't give me answer without
Delta function.
In[240]:=
$Version

Out[240]=
5.0 for Microsoft Windows (June 11, 2003)


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