# Fourier tranform question

1. Dec 11, 2007

### titaniumx3

Fourier transform question

1. The problem statement, all variables and given/known data

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

2. Relevant 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]

3. The attempt at a solution

I've done part (a) and shown that the Fourier transform of $$f(x)$$ is $$4\,{\frac { \left( \sin \left( \pi \,\xi \right) \right) ^{2}}{{\xi}^ {2}}}$$ 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. $${\frac { \left( \sin \left( \xi \right) \right) ^{2}}{{\xi}^{2}}}$$) is slightly different to the Fourier transform I got previously and I'm not sure how to relate them.

Last edited by a moderator: May 3, 2017
2. Dec 12, 2007

### titaniumx3

BTW, I've shown f and it's Fourier transform are both functions of "moderate decrease". I'm also assuming you have to use part (a) to answer part (b). If not, how would you calculate something like that?

Last edited: Dec 12, 2007
3. Dec 12, 2007

:grumpy: