Re: a question about the UnitStep function

*To*: mathgroup at smc.vnet.net*Subject*: [mg58441] Re: a question about the UnitStep function*From*: "Scout" <not at nothing.net>*Date*: Sat, 2 Jul 2005 04:07:01 -0400 (EDT)*References*: <da2msl$944$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi ! I run out the convolution of the square function on Math4 and I've correctly obtained the triangle plot. The analitical output is: 1/4 If [ 1+x<0, (x-2) UnitStep[x-2] - 2x UnitStep[x] + (x+2) UnitStep[x+2], Integrate[ (-UnitStep[-1 + x - z] + UnitStep[1 + x - z]) (-UnitStep[-1 + z] + UnitStep[1 + z]), {z,-Infinity,Infinity} ] ] I Hope help you ~Scout~ "Zhou Jiang" <jiangzhou_yz at yahoo.com> ha scritto nel messaggio news:da2msl$944$1 at smc.vnet.net... > > 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. > >