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Fourier transform question, keep getting zero, minus infinity limit

  1. May 29, 2014 #1
    calculate the fourier transform of the function g(x) if g(x) = 0 for x<0 and g(x) = ##e^{-x}## otherwise.

    putting g(x) into the transform we have:

    ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-ipx} e^{-x} dx##

    which we can write:

    ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-x(ip+1)} dx##

    which will give:

    ##\tilde{g}(p) \propto e^{-x(ip+1)} ## for x between 0 and infinity

    the problem is ##e^{0} = 1## and ##e^{-inf} = 1## so i get zero.

    is there a way around this?

    thanks for any help.
     
  2. jcsd
  3. May 29, 2014 #2

    SteamKing

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    Is ##e^{-∞} = 1##? That would mean ##1/e^{∞} = 1##, which implies ##e^{∞} = 1##.
     
  4. May 29, 2014 #3
    oh dear, so easy, and it took me ages to do all the latex on that op.

    Thanks for clearing this up it's appreciated!
     
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