# unit impulse function

#### 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.

#### Georacer

Joined Nov 25, 2009
5,182
This is valid not only from -infty to infty but to any small region around T.

#### 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).

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

#### Georacer

Joined Nov 25, 2009
5,182
Too true... (Does that expression exist?)

#### narasimhan

Joined Dec 3, 2009
72
Does that expression exist?
Which one? Both expressions in my previous post are valid and have solution(which is already there in my other post).

#### Georacer

Joined Nov 25, 2009
5,182
My question was purely linguistic: The expression at question is "Too true".

#### narasimhan

Joined Dec 3, 2009
72
My question was purely linguistic: The expression at question is "Too true".
Oh I get it.