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
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    What would be the laplace transform of impulse function δ(t +2)
     
  2. shteii01

    AAC Fanatic!

    Feb 19, 2010
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    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

    Well-Known Member

    Jun 17, 2014
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    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
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    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
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    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
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    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

    Well-Known Member

    Jun 17, 2014
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    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
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