unit impulse function

Thread Starter

leftbehind5805

Joined Mar 12, 2010
8
I have a homework assignment where i have to solve several integrals using the unit impulse function. To be honest I am not exactly how to start any of these and the book does not show any examples. Does anyone have a link that shows several examples.

If there are no link with examples, could some one help me figure out the problem below to help me get started
∫δ(T)g(t-T)dT from -infinity to infinity.

any help is appreciated .
Thank you
 

narasimhan

Joined Dec 3, 2009
72
The basic formula ∫x(t)δ(t-T)dt from -infinity to infinity=x(T)
I used signals and systems Oppenheim. At first you'll find it difficult but you'll get the hold of it don't worry.
 

narasimhan

Joined Dec 3, 2009
72
@Georacer for my equation the any small range around T will do. But for the question that the op posted the range is around zero(since the integration is done with respect to T).

@op the answer for your integral is g(t)
hope you could solve the other questions by yourself. if you have any doubts after reading the text do feel free to ask here.
impulse funtion is very important in signals and systems communication dsp etc. so understanding it is very critical.
 

Georacer

Joined Nov 25, 2009
5,182
@Georacer for my equation the any small range around T will do. But for the question that the op posted the range is around zero(since the integration is done with respect to T).
Good point. Thanks for the heads-up. But will that mean that the limits of integration are around zero or around t, whatever that is?
 

narasimhan

Joined Dec 3, 2009
72
limits of integration are around zero
Ya the limits are around zero.

A simple way to remember is that whatever is inside the δ function should be zero.

for ∫x(t)δ(t-T)dt the integral is around T

for ∫δ(T)g(t-T)dT the integral is around zero
 
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