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Homework Help: Help With Fourier Series Expansion of a Periodic Function

  1. Dec 3, 2011 #1
    1. The problem statement, all variables and given/known data

    f(t) defined by f(t) = |t| for (-pi,pi) and f(t+2pi)=f(t)

    the graph is just ^^^

    where w=2pi/T = 1

    2. Relevant equations

    Periodic function using Trigonometric from

    Even Function f(t) = (1/2)anot + (the sum from n=1 to inf) (an)*COS(nwt), where an = 4/T Integrated from 0 to T/2 f(t)*COS(nwt)dt, where T= 2pi

    3. The attempt at a solution

    My answer: I used integration by parts and calculated pi/2 +(the sum from n=1 to inf) (4/(pi)n^2)*COS(nt),

    where anot/2 = 1/T integrated from -T/2 to T/2 f(t)dt, anot=pi

    The book answer has pi/2- [4/pi *the sum from n=1 to inf (1/(2n-1)^2*COS(2n-1)t

    Can anyone tell me if I basically have the same thing?

  2. jcsd
  3. Dec 4, 2011 #2


    User Avatar
    Science Advisor

    No, they are not at all the same thing. Your sum has cos(nt) for all n. The second sum only odd integers times t.
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