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Re: Impulse Fumction using UnitStep???

  • To: mathgroup at
  • Subject: [mg21090] Re: Impulse Fumction using UnitStep???
  • From: "Stephen P Luttrell" <luttrell at>
  • Date: Sun, 12 Dec 1999 23:51:58 -0500 (EST)
  • Organization: Defence Evaluation and Research Agency
  • References: <7hge6f$>
  • Sender: owner-wri-mathgroup at

heiffer <"heiffer"@ozemail.\"nospam\"> wrote in message
news:7hge6f$4dd at
> i am taking a control systems course at university and i am trying to
> evaluate an impulse function [ f[t]=0 except at f[0]=1 for, say a range
> of -5 top 5 ].
> i have managed to get the step and ramp functions going using the
> UnitStep function, but i could not work out the Impulse function. Any
> help would be appreciated.

The impulse function is a DiracDelta, which is a distribution not a
function, so its properties are defined NOT in the form DiracDelta=whatever,
but in the form Integrate[DiracDelta times something, some range or
other]=whatever. The properties of DiracDelta are defined in the
Calculus`DiracDelta` package.

Here is an example of how you use DiracDelta:


In[2]:=Integrate[DiracDelta[x],{x, -Infinity, Infinity}]

In[3]:=Integrate[f[x]DiracDelta[x-a],{x, -Infinity, Infinity}]

Stephen P Luttrell
Signal Processing and Imagery Department
DERA Malvern, St.Andrew's Road
Malvern, United Kingdom, WR14 3PS

+44 (0)1684 894046 (tel)
+44 (0)1684 894384 (fax)
luttrell at (email)

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