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Re: a question about the UnitStep function

• To: mathgroup at smc.vnet.net
• Subject: [mg58440] Re: a question about the UnitStep function
• From: "Mariusz Jankowski" <mjankowski at usm.maine.edu>
• Date: Sat, 2 Jul 2005 04:07:00 -0400 (EDT)
• Organization: University of Southern Maine
• References: <da2msl$944$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Function f has finite support, so use finite limits of integration

Integrate[f[z] f[x - z], {z, -1, 1}]


works fine.


Mariusz






>>> Zhou Jiang<jiangzhou_yz at yahoo.com> 07/01/05 2:12 AM >>>

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.