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Fourier Transform of x*f(x)

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm trying to do the Fourier Transform of "x*f(x)". According to some web sites (http://everything2.com/index.pl?node=fourier transform), it is simply a "property of integration", but I've having some issues.

    2. Relevant equations

    I'm using the form:
    1/2pi int ( x f(x) e ^ (iwx) dx )

    3. The attempt at a solution

    I've tried doing it by parts, but I can't get it to work. My two attempts were:
    1) u=f(x) and dV = x e^(iwx) dx
    2) u=x*f(x) and dV = e^(iwx) dx

    Using 1) I got -1/w^2 dF/dW
    Using 2) I got (1/iw)[-int (e^(iwx) x f'(x) dx) - F(w)]

    I know the answer is -i dF/dw (as it is in the Fourier transform table), but I can't seem to get there. =/
  2. jcsd
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