Re: a question about the UnitStep function

• To: mathgroup at smc.vnet.net
• Subject: [mg58417] Re: a question about the UnitStep function
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Sat, 2 Jul 2005 04:06:13 -0400 (EDT)
• Organization: Uni Leipzig
• References: <da2msl\$944\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

f[x_] := (UnitStep[x + 1] - UnitStep[x - 1])/2;

integrand = PiecewiseExpand[f[z] f[x - z]];

Assuming[Element[x, Reals],
res = Integrate[integrand, {z, -Infinity,
Infinity}]]

??

Regards

Jens

"Zhou Jiang" <jiangzhou_yz at yahoo.com> schrieb im
Newsbeitrag 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.
>
>

```

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