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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: [mg58421] Re: a question about the UnitStep function
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sat, 2 Jul 2005 04:06:18 -0400 (EDT)
  • References: <da2msl$944$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Zhou Jiang schrieb:
> 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. 
>  
> 

Piecewise works well:

In[1]:=
fp[x_] := Piecewise[{{1, -1 <= x <= 1}}, 0];
cv = Integrate[fp[z]* fp[x - z], {z, -Infinity, Infinity}]
Out[2]=
Piecewise[{{2 - x, 0 < x < 2},
           {2 + x, -2 < x <= 0}}, 0]
-- 
Peter Pein
Berlin


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