Compute the coefficients of the Fourier series of the periodic sequences below using the DFT.

(a) \(x^{\prime}(n)=\sin \left(2 \pi \frac{n}{N}\right)\), for \(N=20\).

(b) \(x^{\prime}(n)=\left\{\begin{aligned} 1, & \text { for } n \text { even } \\ -1, & \text { for } n \text { odd. }\end{aligned}\right.\)