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Fourier transform problem

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

    Let a function f on (-[tex]\infty[/tex], [tex]\infty[/tex]) be defined as

    f(x) = cos x, if |x|<1;
    f(x) = 0, otherwise

    Find the Fourier transform of f and then evaluate the integral

    [tex]\int ^{\infty}_{\infty} \frac{sin 2w}{w} cosw dw[/tex]

    2. The attempt at a solution

    I calculate the Fourier transform: [tex]\frac{1}{\sqrt{2 \pi}}(\frac{sin(1-w)}{1-w} + \frac{sin(1+w)}{1+w})[/tex]

    This is the correct answer.

    Now, how can this be used to calculate the integral?
  2. jcsd
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