1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    non

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    That would not be the reason.

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

    In the first case you would not have a factor 2pi, while in the second case you would have a factor 2pi.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fourier transform
  1. Fourier transform (Replies: 4)

  2. Fourier transform (Replies: 1)

  3. Fourier transform (Replies: 1)

  4. Fourier transformation (Replies: 1)

Loading...