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.