1. Limited time only! Sign up for a free 30min personal 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!

Recovering a function using the inverse fourier transform

  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data
    The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and inverse transform.


    2. Relevant equations
    The Fourier and the Inverse Fourier transform integrals


    3. The attempt at a solution
    Do I need to prove the inverse fourier theorem or is there a simpler solution?
    One attempt that I have seen at recovering the original function using the inverse fourier transform formula integrates the exponent part to a sin(Mx)/x type function, which is then shown to approach the delta function as M approaches ∞.
     
  2. jcsd
  3. Sep 4, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Let
    $$F(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty f(t)e^{-i\omega t}\,dt.$$ The problem is simply asking you to show that if you calculate
    $$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty F(\omega)e^{-i\omega t}\,d\omega,$$ you do not recover f(t). Just plug the expression for F(ω) into the second integral and calculate away.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Recovering a function using the inverse fourier transform
Loading...