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Math Help - Inverse Laplace transform

  1. #1
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    Inverse Laplace transform

    Why is it that one finds the degree of numerator always less than that of the denominator when applying inverse laplace transform? For example, Can i find the inverse laplace transform for s^2?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Inverse Laplace transform

    Quote Originally Posted by ajithmk91 View Post
    Can i find the inverse laplace transform for s^2?
    No, because \mathcal{L}\{f(t)\}=F(s)\Rightarrow \lim_{s\to +\infty}F(s)=0
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    Re: Inverse Laplace transform

    I thought the inverse laplace of s^2 was \delta ''(t)
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    Re: Inverse Laplace transform

    But the delta-dirac function seems to violate the formal definition. Is that so?
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    Re: Inverse Laplace transform

    Okay I do a little signal processing, and knowing that s^2 is the LT of the double derivative of the Dirac delta is like Signals 101, very basic. You can google that anyay
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    Re: Inverse Laplace transform

    Quote Originally Posted by rebghb View Post
    Okay I do a little signal processing, and knowing that s^2 is the LT of the double derivative of the Dirac delta is like Signals 101, very basic. You can google that anyay
    Just to thow in my 2 cents....

    First the questions you have asked has multiple different answers and Both correct answers have been given.

    First there is no FUNCTION that satisfies \mathcal{L}\{f(t) \}=s^2.

    Now if you want to use some measure theorey and think of the problem in terms of distributions. http://en.wikipedia.org/wiki/Distribution_(mathematics) and use weak differentation then the solution is correct that it is the 2nd derivative of the delta distribution.

    @rebghb why do you know that it is true? How can it be proved? );
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    Re: Inverse Laplace transform

    Well the s-domain equivelent of the derivitave operator in time is the multiplication by "s". Since the LT of a Dirac delta is 1, then s^2 = s^2*1 is the LT of the double derivaive of the Dirac delta.

    Unfortunately, I do not know how to get this answer from the definition of the transform, I know how to get the LT of a delta but not its derivatives, I would be grateful if you would point that out.

    Thank you
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