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MathGroup Archive 2005

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Re: a question about the UnitStep function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58497] Re: a question about the UnitStep function
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Mon, 4 Jul 2005 02:24:33 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 7/3/05 at 3:57 AM, pdesai1 at umbc.edu (Pratik Desai) wrote:

>Pratik Desai wrote:

>>Zhou Jiang wrote:

>>>Dear Mathgroup, I want to let Mathematica compute the convolution
>>>of two sqare waves. I did as follows

>>>f[x_]:=(UnitStep[x+1]-UnitStep[x-1])/2;

>>>integrand=f[z] f[x-z];

>After seeing other posts, I realize my post was obviously wrong. I
>sincerely apologize for that.  Although my approach using fourier
>transform should work for example if I change my approach as shown
>below, I  get a triangular wave but not what everybody else is
>getting 
>Clear[f,d,d1,h,z]
>f[x_]:=(UnitStep[x+1]-UnitStep[x-1])/2;
>d[\[Omega]_]=FourierTransform[f[x],x,\[Omega]]
>d1[\[Omega]_]=FourierTransform[f[x-1],x,\[Omega]]
>h[x_]=InverseFourierTransform[d[\[Omega]]*d1[\[Omega]]//FullSimplify,\[Omega], 
>x]
>Plot[h[x],{x,-10,10}]


If you look carefully at the original poster's integrand, you will see he is convolving f with itself. So, I think your h needs to be

h[x_]=InverseFourierTransform[(d[\[Omega]])^2//FullSimplify,\[Omega], x]
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