Re: Impulse Fumction using UnitStep???

• To: mathgroup at smc.vnet.net
• Subject: [mg21090] Re: Impulse Fumction using UnitStep???
• From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
• Date: Sun, 12 Dec 1999 23:51:58 -0500 (EST)
• Organization: Defence Evaluation and Research Agency
• References: <7hge6f\$4dd@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```heiffer <"heiffer"@ozemail.\"nospam\".com.au> wrote in message
news:7hge6f\$4dd at smc.vnet.net...
> 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[1]:=Needs["Calculus`DiracDelta`"]

In[2]:=Integrate[DiracDelta[x],{x, -Infinity, Infinity}]
Out[2]=1

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

--
Stephen P Luttrell
Signal Processing and Imagery Department
Malvern, United Kingdom, WR14 3PS

+44 (0)1684 894046 (tel)
+44 (0)1684 894384 (fax)
luttrell at signal.dera.gov.uk (email)

```

• Prev by Date: Cutting and pasting table to ascii file
• Next by Date: 2 coupled diff. eqns
• Previous by thread: Re: Cutting and pasting table to ascii file
• Next by thread: 2 coupled diff. eqns