Calculating the inverse Fourier transform of two given functions

Question

I need to calculate the inverse Fourier transform of the following functions:

1. $\displaystyle f(w) = e^{(-\pmb{i}5w)} * {\rm sinc}(2w) $

2. $\displaystyle g(w) = \frac{\pmb{i}w}{(3+\pmb{i}w)(1+\pmb{i}w)} $

I'm really stuck and I don't know where to start, any help would be appreciated!

Answer 1

Here are some hints:

1) If $e_t(x)= e^{itx}$,what is $\widehat{e_tf}$?

2) What is $\widehat{f'}$?

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Also note that it is important to state the exact definition of the Fourier transform if you wish to compute explicit functions.

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