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Calculating Fourier Coefficients

  1. Nov 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine the fourier coefficients of the 3-periodic function and determine how many terms needed to keep 3 digit accuracy.

    f(t) = 1/2(1-Cos[Pi t]), for 0<t<1
    f(t) = 1, for 1<t<2
    f(t) = 1/2(1-Cos[Pi(t-3)]), for 2<t<3



    2. Relevant equations
    For the cos coefficient:
    ak = [tex]\frac{2}{3}\int Cos(\frac{2 \pi k t}{3}) * f(t)[/tex]

    I used the identity: 2 Cos[a] Cos= Cos[a+b] +Cos[a-b]


    3. The attempt at a solution

    The problem is, when I work out the integrals I get an expression similar to:
    [tex]\frac{a k +b}{c k}Sin()[/tex]

    I used the identity above and got a lot of cos integrals that were easy to solve
    However the answer is:
    ak = [tex]\frac{-4 k}{\pi(9-4 k^{3}}Sin(\frac{2 \pi k}{3})[/tex]

    I am not sure how the k^3 comes into play, since all of the integrals were straight forward and only produced one power of k in the denominator. The only thing i can think of is that I didn't pick the correct trig identity.
     
  2. jcsd
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