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I [Signal and system] Function with fourier series a[k] = 1

  1. Dec 13, 2017 #1
    We have:
    Period T = 4, so fundamental frequency w0 = pi/2.
    This question seems sooo easy. But when I use the integral:

    x(t) = Σa[k] * exp(i*k*pi/2*t).
    I get 1 + sum(cos(k*pi/2*t)), which does not converge.

    Where did I went wrong ?
    Thanks a lot for your help.
     
    Last edited: Dec 13, 2017
  2. jcsd
  3. Dec 13, 2017 #2

    BvU

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    Hello Duke,

    I have no idea :wink: what your T and w0 stand for. Especially T. Have you heard of the dirac delta function ? Familiar with distributions ?
     
  4. Dec 13, 2017 #3
    Thanks for replying!! I edited the post. So the answer for this question is:
    y(t) = ∑(delta(t - 4k))
    From y(t) i can show that a[k] = 1 for all k. But I couldn't find y(t) given that a[k] = 1 since it didn't converge.
     
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