• Support PF! Buy your school textbooks, materials and every day products Here!

Fourier tranform question

  • Thread starter titaniumx3
  • Start date
  • #1
53
0
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!
 
Last edited by a moderator:

Answers and Replies

  • #2
53
0
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:
  • #3
53
0
:grumpy:
 

Related Threads for: Fourier tranform question

  • Last Post
Replies
3
Views
1K
Replies
2
Views
554
  • Last Post
Replies
4
Views
829
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Top