$x(t)=9+8cos(1200t)+7cos(600t-0\mathrm{.}7)$

The system function for the LTI system is

$H(z)=\frac{(1+z^{-1})(1-e^{j0\mathrm{.}3}{z}^{-1})(1-e^{-j0\mathrm{.}3}{z}^{-1})}{(1-0\mathrm{.}8e^{j0\mathrm{.}6}{z}^{-1})(1-0\mathrm{.}8e^{-j0\mathrm{.}6}{z}^{-1})}$

If $f_s=4000$ samples$/$s$,$ determine $y(t),$ the output of the D$-$to$-$C converter.