Frequency spectrum of a sinc function I am doing one example from my book as a preparation for exam.

The assignment is:


  It is given that: 
  $$\mathbb{rect}(t)=pf(t) \leftrightarrow PF(f)=2AT_0 \cdot \mathbb{sinc}(2\pi fT_0)$$
  you need to calculate frequency spectrum of:
  $$pf(t)=\mathbb{sinc}(\omega t)$$


Truthfully, I have no idea where to start. I presume that the solutions is absolute value of sinc function, because I read it from solution, but in the solution there was only diagram.

I tried to solve directly using Fourier transformation on sinc function, but I got very messy equation at the end.

So, my question is: How can I solve this assignment?

Thanks you very much!!!

EDIT:
I found this pdf, on the 7(162) side it explains what I want to do, but this is only with pictures. I want to understand it. 
http://ultrasound.ee.ntu.edu.tw/classnotes/ckt2/Chapter12.pdf
Look at the forms of the functions, and remember the duality property.

I invite you the read the Wikipedia article: http://en.wikipedia.org/wiki/Fourier_transform