# Fourier Series Coefficients for Signals

The question is:
We specify the fourier series coefficients of a continuous-time signal that is periodic with period 4. Determine the signal x(t).
$a_k=\begin{cases} 0, & k=0\\ j^k\frac{sin\frac{k\pi}{4}}{k\pi}, & \text{otherwise } \end{cases}$

I have no idea where to even begin on this one. I've been able to do fourier series calculations on already given signals, but I have no idea how to work backwards now. Any ideas?

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Is $j$ the imaginary unit? Also, the $a_k$ are the coefficients multiplying what basis ($\sin,\,\cos\,e$)? –  Pragabhava Oct 18 '12 at 3:47
@Pragabhava yes j is the imaginary unit. –  Charlie Yabben Oct 18 '12 at 3:53
And how are the $a_k$'s calculated, do you use the form $$a_k = \frac{1}{T}\int_0^T x(t) e^{-j 2\pi \frac{k}{T} x} dx$$ where $T$ is the period? –  Pragabhava Oct 18 '12 at 14:53