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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: [mg58438] Re: [mg58411] a question about the UnitStep function
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Sat, 2 Jul 2005 04:06:57 -0400 (EDT)
  • References: <200507010602.CAA09193@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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];
> 
>Assuming[Element[x, Reals], Integrate[integrand, {z, -Infinity, Infinity}]]
> 
>Mathematica gave me the result as follows,
>((-1 + x) UnitStep[-1 + x] - x UnitStep[x] + (2 + x) UnitStep[2 + x])/4
> 
>I plot the result to check 
> 
>Plot[%,{x,-10,10}, PlotRange->All];
> 
>It is clear wrong since the convolution of two square waves should be convergent. Can anyone give me some help with the subtlties about the UnitStep function? Any thoughts are appriciable. 
> 
>
>  
>
Try this,
f[x_]:=(UnitStep[x+1]-UnitStep[x-1])/2;
integrand1=f[x] f[x-1]
d[\[Omega]_]=FourierTransform[integrand1,x,\[Omega]]//ExpToTrig//Simplify
g[x_]=InverseFourierTransform[Evaluate[d[\[Omega]]],\[Omega],x]
DisplayTogether[Plot[f[x],{x,-10,10}],Plot[f[x-1],{x,-10,10}]]
Plot[g[x],{x,-10,10}]

Hope this is what your are looking for

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



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