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Fourier transform

  1. Nov 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the Fourier transform of the function f(x) = 1 if -1<x<1, f(x) = 0 otherwise

    2. The attempt at a solution

    [tex]\hat{f}(w) = \frac{1}{\sqrt{2 \pi}} \int ^{1}_{-1}e^{-iwx}dx = \frac{1}{\sqrt{2 \pi}} [\frac{e^{-iwx}}{-iw}]^{1}_{-1} = \frac{1}{-iw \sqrt{2 \pi}}(e^{-iw} - e{iw}) = \sqrt{\frac{2}{\pi}} \frac{sinw}{w}[/tex]

    According to my book, the correct answer is [tex]\sqrt{\frac{\pi}{2}} \frac{sinw}{w}[/tex]

    Who is right?
  2. jcsd
  3. Nov 29, 2008 #2
    I can't find any mistakes in your solution.
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