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?

**Follow-Ups**:**Re: Re: difference between HeavisidePi and UnitBox***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>