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 formulation of the dirac delta

  1. Aug 1, 2007 #1
    I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is
    [tex] \int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f) [/tex]

    and the one in my textbook (Robinett) is

    [tex] 1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f) [/tex]

    I do not understand how they are equivalent? How can you just take the 2pi out of the integral?
  2. jcsd
  3. Aug 1, 2007 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's a simple change of variable: if [itex]t'=2\pi t[/itex], then [itex]dt=dt'/2\pi[/itex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Fourier transform formulation of the dirac delta
  1. Dirac delta (Replies: 6)

  2. Dirac delta (Replies: 4)

  3. Dirac delta (Replies: 24)

  4. Dirac delta (Replies: 8)