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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

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    It's a simple change of variable: if [itex]t'=2\pi t[/itex], then [itex]dt=dt'/2\pi[/itex].
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