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Question about the Dirac Delta Function

  • Thread starter xoxomae
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  • #1
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Homework Statement


Find the Fourier spectrum of the following equation

Homework Equations


##F(\omega)=\pi[\delta(\omega - \omega _0)+\delta(\omega +\omega_0)]##

The Attempt at a Solution


Would the Fourier spectrum just be two spikes at ##+\omega _0## and ##-\omega _0## which go up to infinity?
 

Answers and Replies

  • #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
 
  • #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.
 
  • #4
rude man
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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.
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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