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.