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Laplace transform and fourier transform

  1. Jun 8, 2012 #1
    1. The problem statement, all variables and given/known data
    F{f(t)} is the fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t)

    why F{f(t)} = L{f(t)} where s = jw in L{f(t)}


    3. The attempt at a solution
    I suppose the definition of F{f(t)} is

    ∫[f(t)e^-jwt]dt

    where the lower integral limit is -∞ and higher intergral limit is +∞.

    And I suppose the definition of L{f(t)} is

    ∫[f(t)e^-st]dt

    where the lower integral limit is -∞ and higher integral limit is +∞.(that is bilateral Laplace transform)

    and i think it is obviously to say F{f(t)} = L{f(t)} where s = jw in L{f(t)} just by substitute s = jw in ∫[f(t)e^-st]dt.

    My solution is so simple that I can't believe it's a problem assigned by my professor!
    Some guy please tell me if I am correct or not, and where it is.

    Any reference or advise will be appreciated.

    thanks in advance.
     
  2. jcsd
  3. Jun 9, 2012 #2
    Yes you are correct, as long as the imaginary axis is inside the region of convergence.
     
  4. Jun 11, 2012 #3
    3x~ I am more confident~
     
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