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**Fourier transform question**

## Homework Statement

http://img410.imageshack.us/img410/852/question3jh8.gif [Broken]

## Homework Equations

I will be using the following definitions and theorems:

http://img338.imageshack.us/img338/4173/moderatedecreasevd4.gif [Broken]

http://img260.imageshack.us/img260/7461/fouriertransonmodzo5.gif [Broken]

http://img338.imageshack.us/img338/3530/plancherelmodvv2.gif [Broken]

## The Attempt at a Solution

I've done part (a) and shown that the Fourier transform of [tex]f(x)[/tex] is [tex]4\,{\frac { \left( \sin \left( \pi \,\xi \right) \right) ^{2}}{{\xi}^

{2}}}[/tex] but on part (b) I am a bit lost. I know how to apply Plancherel's theorem but the function inside the modulus (i.e. [tex]{\frac { \left( \sin \left( \xi \right) \right) ^{2}}{{\xi}^{2}}}[/tex]) is slightly different to the Fourier transform I got previously and I'm not sure how to relate them.

Please help!

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