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.

**Follow-Ups**:**Re: a question about the UnitStep function***From:*Pratik Desai <pdesai1@umbc.edu>