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 DERA Malvern, St.Andrew's Road Malvern, United Kingdom, WR14 3PS +44 (0)1684 894046 (tel) +44 (0)1684 894384 (fax) luttrell at signal.dera.gov.uk (email)