a.
$ \begin{align} X[k]&=\sum_{n=0}^3 x[n]e^{-j\frac{2\pi n}{N}k} \\ &=\sum_{n=0}^3 cos(\frac{n\pi}{2})e^{-j\frac{2\pi n}{N}k} \\ &=1-e^{-j\pi k}\text{ , }0\le k\le 3 \end{align} $
b.
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