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


2 Answers 2


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

  • $\begingroup$ 404 for "duality property" link $\endgroup$
    – jojeck
    Commented Jun 21, 2014 at 19:15

Note the relationship of calculating the Fourier Transform to that of calculating the inverse Fourier Transform. If you already have one result, what does that say about computing the other?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.