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Homework Help: Fourier transform

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data

    if y(ω) = F{x(t)}, what is F{y(t)} (F is the fourier transform operation)

    2. Relevant equations


    3. The attempt at a solution

    I tried finding F^-1{y(ω)}, which is equal too x(t), but I could not go on with finding F{y(t)}
  2. jcsd
  3. Feb 25, 2012 #2

    I like Serena

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    Hi homad2000! :smile:

    Check the section on "duality" on the wiki page: http://en.wikipedia.org/wiki/Fourier_transform
    It says what the transform is of a transform with the domain swapped.
  4. Feb 25, 2012 #3
    Ok, correct me if I'm wrong:

    I got F{y(t)} = x(-ω) ? or should I add the 2π to that?
  5. Feb 25, 2012 #4

    I like Serena

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    Yep. That's it.

    Whether or not 2π should be added depends on the definition of your Fourier transform.
    As you can see on the wiki page, there are 3 different common definitions.
    Which of the 3 does your text book use?
  6. Feb 25, 2012 #5
    I believe i should add the 2 pi, because we use w = 2 * pi * f

    Thank you for your help, I appreciate it :)
  7. Feb 25, 2012 #6

    I like Serena

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    That would not be the reason.

    Your Fourier transform would be defined as either:
    $$F(\omega)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} f(t) e^{-i \omega t}\, dt$$
    $$F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-i \omega t}\, dt$$

    In the first case you would not have a factor 2pi, while in the second case you would have a factor 2pi.
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