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Question about the Dirac Delta Function

  1. Apr 14, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the Fourier spectrum of the following equation

    2. Relevant equations
    ##F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]##

    3. The attempt at a solution
    Would the Fourier spectrum just be two spikes at ##+\omega _0## and ##-\omega _0## which go up to infinity?
     
  2. jcsd
  3. Apr 14, 2016 #2

    BvU

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    Yes. My guess is you are supposed to find the function that has such a Fourier transform ?
    When you carry out the integration to find that functionl the ##\delta## functions will behave decently -- check the definition of a delta function
     
  4. Apr 14, 2016 #3

    George Jones

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    xoxmae already has a function ##F\left( \omega\right)## that has two "spikes", one at ##\omega = \omega_0## and one at ##\omega = -\omega_0##. The Fourier transform of this will not have spikes.
     
  5. Apr 22, 2016 #4

    rude man

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    He didn't ask for the Fourier transform of F(ω). He asked for the spectrum, i.e. a graph in the frequency domain, which is what BvU said, except it's not sufficient to say " ... spikes which go up to to infinity ..." of course. What of the ω coefficient?

    I also agree with BvU that the problem was more likely to find the inverse transform of F(ω).
     
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