Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Definition clarification for Fourier transform

  1. Sep 20, 2015 #1
    I have been studying Fourier transforms lately. Specifically, I have been studying the form of the formula that uses the square root of 2π in the definition. Now here is the problem:

    In some sources, I see the forward and inverse transforms defined as such:
    F(k) = [1/(√2π)] ∫-∞ f(x)eikx dx
    f(x) = [1/(√2π)] ∫-∞ f(k)eikx dk


    In other cases, I've seen:
    F(k) = [1/(√2π)] ∫-∞ f(x)e-ikx dx
    f(x) = [1/(√2π)] ∫-∞ f(k)eikx dk

    Notice that in the first version of the forward transform (the one that solves for F(k)), the exponential in the integrand has a positive sign in the exponent ikx, while in the 2nd version it has a negative ikx.

    Which version is correct? Are they both correct and it is a matter of convention? Are neither correct?

    Also, is there some way to do a multiple dimensional Fourier transform using volume integrals? If so, what is the formula for that (preferably including (√2π))?
     
  2. jcsd
  3. Sep 20, 2015 #2
    Only the 2nd pair is correct. There are a couple conventional issues, but no matter what the sign on the exponent has to change for the inverse transform relative to the forward transform.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Definition clarification for Fourier transform
  1. Fourier transform (Replies: 2)

  2. Fourier transforms (Replies: 1)

  3. Fourier transform (Replies: 1)

  4. Fourier transform (Replies: 1)

Loading...