# laplace transform of time shifted function(t+T)

Discussion in 'Homework Help' started by hamza324, Mar 4, 2016.

1. ### hamza324 Thread Starter Member

Jul 10, 2011
33
1
What would be the laplace transform of impulse function δ(t +2)

2. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,516
515
It, seems to me, that it is not a causal function, therefore the Time Shifting property of Laplace Transform does not apply.

hamza324 likes this.
3. ### WBahn Moderator

Mar 31, 2012
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Are you using a one-sided Laplace Transform?

4. ### MrAl Distinguished Member

Jun 17, 2014
2,573
521
Hello,

Is this question just a curiosity or did it arise from some physical situation or test question?

5. ### hamza324 Thread Starter Member

Jul 10, 2011
33
1
It was just a question in my homework assignment.
The question was simply as: find the laplace tranform of the above mentioned function.
I will post the answer here when i get the right solution.

6. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
If you are using a single sided transform, the (non-zero) transforms only exist for those portions of a waveform that are present for t > 0-.

7. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
You might see what it is by simply applying the definition of the one-sided Laplace transform to a unit impulse that occurs prior to t = 0.

8. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,516
515
WBahn is correct.
If you are doing single sided transform, from 0- to positive infinity, then the impulse function you have does not meet causality requirement and you can not use time shifting property of Laplace Transform.

However, if your interval is from negative infinity to positive infinity, then you can simply apply the definition and find answer mathematically.

9. ### MrAl Distinguished Member

Jun 17, 2014
2,573
521
Hi,

Ok thanks.

We might also need some proof to go with that. I mention this because the definitions i see all state the same thing, that for the constant (usually given as 'a') it has to be greater than or equal to zero, and it is subtracted as in f(t-a), so f(t+a) with 'a' positive or f(t-a) with 'a' negative would not meet the requirement for the time shift theorem. I'm still open to new ideas though so see what you can dig up.
It could be that if we do it one way we get -e^-as and if we do it another way we get +e^-as. I wont press this point just yet though.

Last edited: Mar 7, 2016