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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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