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Duality and Fourier Transform

  1. Nov 15, 2011 #1
    1. The problem statement, all variables and given/known data
    How do I use the [itex](FF(f))(x)=2\pi f(-x)[/itex] where [itex]F[/itex] is the Fourier transform.
    and [itex]F(f(x-a))(k)=\exp(-ika) X(k)[/itex] where [itex]X(k)=F(f(x))[/itex]

    to get [itex]F(\exp(iax)f(x))(k)=X(k-a)[/itex]

    2. Relevant equations

    Please see above.

    3. The attempt at a solution
    The variables confuse me. I can do it by brute force plugging and chugging but I really don't see how to do it using the duality property...
     
  2. jcsd
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