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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