Find function given its complex Fourier series

Question

The complex Fourier series coefficients of a function with periodicity 4 are as follows: $$C_k=\frac{\sin{k\frac{\pi}{8}}}{2k\pi}$$ Find this function.

I really have no idea how to solve this problem.

Answer 1

The Fourier series coefficients of Rectangular signal with amplitude $A$ is :

$\frac{A}{T}\frac{sin(\frac{k\pi}{T})}{\frac{k\pi}{T}}$. If you compare this with your given coefficient you can find the parameter of the rectangle.