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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

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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

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  • $\begingroup$ 404 for "duality property" link $\endgroup$ – jojek Jun 21 '14 at 19:15
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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?

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