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Continuous Time Fourier Series of cosine equation

  1. Nov 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Using the CTFS table of transforms and the CTFS properties, find the CTFS harmonic function of the signal

    2*cos(100*pi(t - 0.005))

    T = 1/50

    2. Relevant equations

    To = fundamental period

    T = mTo

    cos(2*pi*k/To) ----F.S./mTo---- (1/2)(delta[k-m] + delta[k+m])

    3. The attempt at a solution

    using the table of pairs and CTFS properties, the solution I arrived to was:

    1) Cx[k] = (delta[k - 1] + delta[k+1])*e^(-j*0.5*pi*k)

    My solution is right but the final solution from the solution manual there's one more step to simplify it even more:

    2) Cx[k] = j*(delta[k - 1] + delta[k+1])


    How did they go from (1) to (2) ?
     
  2. jcsd
  3. Nov 14, 2015 #2
    Anyone?
     
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