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Suppose you are given the following information about a continuous-time periodic signal, $x(t)$, with period $6$ and its Fourier series coefficients $(a_k)$, (1)-(4). Using the synthesis equation, your knowledge of the Fourier series representation of common signals and the properties of continuous-time Fourier series (see Table 3.1 from text), determine the function $x(t)$.

  1. $a_k = a_{k-3}$
  2. $\int_{-1}^5 x(t)dt = 3$
  3. $\int_{-1}^3 x(t)dt = 5$
  4. $\int_{-1}^1 x(t)dt = i$

I really don't even know where to start...I can't find any examples like this.

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This looks like a homework problem. What text are you using? You should also tag this with the homework tag. – mike4ty4 Oct 4 '12 at 3:11

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