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Existence oF Fourier Co-efficient

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data

    Let f(t) be a signal whose time period is T.

    1. if f(t+T/2)=f(t) proof that the fourier series representation will contain no odd harmonics
    2. if f(t+T/2)=-f(t) proof that the fourier series representation will contain no even harmonics

    2. Relevant equations

    3. The attempt at a solution

    1. I tried to proof that for f(t+T/2)=f(t) odd fourier co-efficient is zero . But I can not prove that .
  2. jcsd
  3. Jan 31, 2012 #2
    You should write down the definition of the fourier series coefficients. Then take a good look at them and try to argue that they are 0 for odd numbers, given that f(t+T/2)=f(t). If you can't figure it out: what is the definition of the coefficients?
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