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I have a question about F. transforms. In my exams (for mathematical methods in physics) I'm usually given a function such as:

[tex]f(t)=\begin{cases} 1,\ t\in(-T,T)\\

0,\ else\\

\end{cases}[/tex]

Now I can find easily [tex]F(\omega)[/tex], but then I need to find the original function again (to confirm the validity of the found transform). And when I integrate I'm converting it into complex integral. And there are the troubles! I end up with exponential functions, but since t is arbitrary I can choose two contours of integration. And the question is: based on what do I choose those contours? Do I have to make it such that I have decaying exponential? My assistant wasn't quite clear on that and I didn't find it anywhere else...

So if anyone could help me I'd appreciate it! Thanx!

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# Question about Fourier Transforms

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