I am studying about the randomprocess thesedays.

I am stuck on solving the discrete signal to show the fourier transform

the formula is that

$$ w_b(k) = {N-|k|\over N} \quad \quad when\ \ |k| <= N $$

$$ w_b(k) = 0 \ \ \ \quad \quad \quad else where $$

and the problem is the fourier transform of $w_b(k), i.e \ W_B(f)$.

I check the answer is

$$ W_B(f) = {1\over N}[sin(N*pie*f)/sin(pie*f)]^2$$

But I couldnt figure out the process of this fourier transform

Please help me for solving this

  • $\begingroup$ No need to repeat: math.stackexchange.com/questions/119302/… $\endgroup$ – grdgfgr Jun 1 '15 at 12:54
  • $\begingroup$ @grdgfgr I should find more and more :) Thank you very much $\endgroup$ – user2874612 Jun 2 '15 at 1:01
  • $\begingroup$ @grdgfgr May I ask you the process of getting a final answer? $\sum_{n=1}^{N-1} {(N-n)\over N}cos(wn) $ I saw the page you linked, but it is too simple to understand for me $\endgroup$ – user2874612 Jun 2 '15 at 1:51
  • $\begingroup$ I posted another answer there, to address your question. $\endgroup$ – user147263 Jun 2 '15 at 5:08
  • $\begingroup$ @user2874612 Would I be correct in assuming that the trouble you have with this is not related with fourier transformation but rather with dealing with summation? $\endgroup$ – grdgfgr Jun 2 '15 at 6:43