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