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MathGroup Archive 2005

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a question about the UnitStep function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58411] a question about the UnitStep function
  • From: Zhou Jiang <jiangzhou_yz at yahoo.com>
  • Date: Fri, 1 Jul 2005 02:02:03 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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. 
 


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