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.

Proposed Steps to get the Answer

The first step is to figure out the period N of x[n].

.....please fill in....

Then, one needs to find the coefficients using the summation formula

$ \begin{align} a_n &= \frac{1}{T} \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \text{ by the definition of Fourier series coefficients,} \\ & = ...\\ & = ... \text{ please finish } \end{align} $

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