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Another Fourier Inversion Problem

  1. Jun 4, 2006 #1
    Find the inverse transform of

    [tex]
    \frac{\sin{a\omega}}{\omega}
    [/tex]

    I know the step function has a transform of this form, so I as able to find the inverse transform by assuming it was some step function and then looked for the right constants.

    However, I would like to also know how to do it by the definition:

    [tex]
    f(x) = \frac{1}{2\pi} \lim{\int{\overline{f}(\omega)e^{-i\omega x} d\omega}}
    [/tex]

    Where the limit is L--> infinity and the integration limits are -L to +L.

    I think this must be done by contour integration? Can someone show me how to setup the contour integral?
     
  2. jcsd
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