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Fourier Transform sin x / x,

  1. May 27, 2006 #1
    Hi, how do I find the fourier transform of this function sin x / x, i.e.,

    f* = Integral( sin x / x * exp( i*w*x) dx from -infinity to +infinity ).

    I've been using Jordan's Lemma up to this point, but it doesn't seem to
    apply here as a way to evaluate the integral.

    Thanks for any help.
     
  2. jcsd
  3. May 27, 2006 #2
    Hint: Use the duality property of Fourier transforms. Remember that d*sinc(w) = d*sin(pi*w*d) / (n*pi*w*d) is the fourier transform of a square wave in the time domain with duty cycle d.

    Edit: Fixed some things. If the time domain part confuses you, ignore it; I learned this stuff primarily from a signals & systems perspective.
     
    Last edited by a moderator: May 27, 2006
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