Fourier transform of exp(-|t|) with odd and even functions

[Niles]

[SOLVED] Fourier transforms

Homework Statement

Please take a look at the following:

http://books.google.dk/books?id=9p6...M_p7C1N&sig=M8eywUTmbsWbFY6OCqSth13LWFE&hl=da

I have shown that the Fourier transform of f(t) = exp(-|t|) = $$\sqrt{\frac{2}{pi}}\cdot \frac{1}{1+\omega ^2}$$.

Now I am having trouble with question A. I know what the inverse Fourier transform is given by, but the we have an odd function (exp(iwt)) multiplied to an even function (the above). This results in an odd function, so how do I rewrite it?

 

[Niles]

Ok, I read something about the inverse Fourier transform of an even function, and it adds up now. Problem solved.