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}
]
]

~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.
>
>

```

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