Do $7\mathrm{.}5-17$

$7\mathrm{.}5-16.$ Extend Example $7\mathrm{.}5-4$ by showing that the autocorrelation function for the continuous$-$time process having the power spectrum

$S_{xx}()=Kco{s}^2(\frac{}{2W_x})rect(\frac{}{2W_x})$

is

$R_{xx}()=\frac{K{W}_x}{4}[2Sa(W_x)+Sa(W_x-)+Sa(W_x+)]$

$=\frac{(K{W}_x\frac{}{2})sin(W_x)}{W_x[{}^2-(W_x{)}^2]}$

$7\mathrm{.}5-17.$ Rework Example $7\mathrm{.}5-5$ except assume the random process defined in Problem $7\mathrm{.}5-16.$ Rework your results for $N=10$ and compare to the results for $N=5.$

Example $7\mathrm{.}5-5$ asking for the power spectrum of the DT random process

Do $7\mathrm{.}5-17$