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Homework Help: Fourier Series of a constant (Pi)?

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Determine the Fourier series of f(x) = pi + x

    2. Relevant equations

    3. The attempt at a solution
    I see you have to calculate the two "series" separately and then add them. I know that the Fourier series of pi is just pi - but i was wondering why (i know that sounds ridicolous).

    Is it simply a case of, pi is not perioidic so cant be expanded as a Fourier series so its just pi?

    Or can you (as i have been trying and failing to do), somehow plug into the Fourier equations (for bn) show that the series is zero, but the a0 is 2pi, so its just pi?

    Just interested is all....

  2. jcsd
  3. Apr 26, 2010 #2
    The Fourier transform of a constant is that constants times the delta function, which is not really a function but a distribution (I'm assuming you're working over all of R).
  4. Apr 26, 2010 #3


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    You don't have to calculate them separately.
    A constant function f(x)=c is periodic because f(x)=c=f(x+T).
    Yes, that's exactly what you do.
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