How to Use Duality Property for Finding Fourier Transform of sin x / x?

[eckiller]

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.

 

[vsage]

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.