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MathGroup Archive 2004

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Re: Piecewise functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51607] Re: Piecewise functions
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Wed, 27 Oct 2004 01:54:12 -0400 (EDT)
  • References: <cl9tau$7oi$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Luca,

perhaps it helps in constructing your piecewise function if you use the 
following function which is unity in the interval [a,b] (assume a>b) and 
zero elsewhere

f[x_]:= UnitStep[x-a] * UnitStep[b-x]

This can also be written in linear form as

g[x_]:= UnitStep[x-a] - UnitStep[x-b]

Now you have each interval available for your definition.

If you like you can test it e.g. with
In[335]:=
a = -2; b = 3;
Clear[f]
f[x_] := UnitStep[x - a]*UnitStep[b - x]
Plot[f[x], {x, a - 1, b + 1}];
Clear[g]
g[x_] := UnitStep[x - a] - UnitStep[x - b]
Plot[g[x], {x, a - 1, b + 1}];

Remark 1: the linear form (g) should be used as it facilitates the work 
for mathematica

Remark 2: I noticed (alas!) that Integrate does not work properly for 
piecewise functions (even is they have a continuous derivative) without 
UnitStep. Hence I strongly recommend using it.

Wolfgang

Luca wrote:

> Hi all. I'm studying for the exam of signals and systems and I was
> trying to plot some kind of functions I transformed for exercise. So, I
> need to plot piecewise functions like:
> 
> y(x) = x if x > 3
> y(x) = -x if -1 < x < 3
> y(x) = 1 else
> 
> (should have been a system).
> I found out in the guide the chapter about this, and I learned that it
> is possible with the function UnitStep, which I know. Anyway, I found
> it difficult to determine the equation of the function using this
> method. Is it possible to do it simply writing everything like I did
> before, more or less? i.e. without having to determine the equation
> with the UnitStep function.
> Hope I've been clear enought. Many thanks.
> 
> Luca
> 
> 


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