Re: difference between HeavisidePi and UnitBox

• To: mathgroup at smc.vnet.net
• Subject: [mg100364] Re: difference between HeavisidePi and UnitBox
• From: Anatoly <anatoly.bourov at gmail.com>
• Date: Tue, 2 Jun 2009 06:41:28 -0400 (EDT)
• References: <gvq08j\$moo\$1@smc.vnet.net> <gvtmcu\$gc6\$1@smc.vnet.net>

```I understand that it doesn't matter.  There's even some discussion
here about it http://mathworld.wolfram.com/RectangleFunction.html

My question is regarding "The piecewise version of the rectangle
function is implemented in Mathematica as UnitBox[x], while the
generalized function version is implemented as HeavisidePi[x]."

why do we need both?  I find the integral transforms (I use mostly
FourierTransform) actually work much better with the piecewise UnitBox
for 5-bar patterns that I like to use.

Does anyone have a thorough explanation of when generalized functions
are better than piecewise and vice versa?

-Anatoly

On May 31, 6:33 pm, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de>
wrote:
> Hi,
>
> what happens at x->1/2  and x->-1/2 with HeavisidePi[] and UnitBox[] ?
>
> For distributions like HeavisidePi[] that are used
> inside of an integral the single
> point does not matter. For functions like UnitBox[] it may be important.
>
> Regards
>    Jens
>
>
>
> Anatoly wrote:
> > I am a very new user, and am not quite clear on the difference between
> > general (HeavisidePi) and numerical (UnitBox, or piecewise) functions.
>
> > When I try to create a 5-bar pattern using one of these and apply a
> > FourierTransform, I have varying degrees of success...
>
> > With HeavisidePi I can create an infinite series of them and
> > FourierTransform has no problems, but it doesn't like modifying the
> > argument as in HeavisidePi(x/w)
>
> > With UnitBox I have the opposite issue.
>
> > Is there a clear explanation on the difference between the two groups
> > of functions, and when I should use which?

```

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