Exercise: Compute the DT Fourier series coefficients of the following discrete-time signal:

$x[n]=\sum_{k=-\infty}^\infty \left( u[n-5k]-u[n-4-5k] \right)$

After you have obtained the coefficients, write the Fourier series of x[n].

Help: If the function above does not look periodic to you, please read this page.

Answer

Can somebody finish the following computation?

$\begin{align} a_n &= \frac{1}{T} \sum_{2\pi} x[n] e^{-j \frac{2\pi}{T}nk} \\ & = ...\\ \end{align}$

not finished, I'll come back to this later. @_@

-Ty