- #1
titaniumx3
- 53
- 0
Fourier transform question
http://img410.imageshack.us/img410/852/question3jh8.gif
I will be using the following definitions and theorems:
http://img338.imageshack.us/img338/4173/moderatedecreasevd4.gif
http://img260.imageshack.us/img260/7461/fouriertransonmodzo5.gif
http://img338.imageshack.us/img338/3530/plancherelmodvv2.gif
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!
Homework Statement
http://img410.imageshack.us/img410/852/question3jh8.gif
Homework Equations
I will be using the following definitions and theorems:
http://img338.imageshack.us/img338/4173/moderatedecreasevd4.gif
http://img260.imageshack.us/img260/7461/fouriertransonmodzo5.gif
http://img338.imageshack.us/img338/3530/plancherelmodvv2.gif
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!
Last edited by a moderator: