What will be power spectral density?

Question

If the autocorrelation of a random process is given as $$r_x(k) = \begin{cases} 10 - \vert k \vert &\mbox{if } |k| < 10 \\ 0& \mbox{else.} \end{cases} $$ What will be the DTFT of this random process?

Answer 1

\begin{align*} R\left(\omega\right) & =\sum_{k=-9}^{9}\left(10-\left|k\right|\right)e^{-ik\omega}=\left(\frac{\sin\left(5\omega\right)}{\sin\left(\omega/2\right)}\right)^{2} \end{align*}