(Solved): 1) (20pts) Consider a discrete time system described by the difference equation \[ y(k)-\frac{3}{2 ...

1) (20pts) Consider a discrete time system described by the difference equation \[ y(k)-\frac{3}{2} y(k-1)+\frac{1}{2} y(k-2)=r(k-1)+\frac{1}{2} r(k-2) \] where \( \mathrm{y}(\mathrm{k}) \) is the system output and \( \mathrm{r}(\mathrm{k}) \) is the system input. If \( r(k)=u(k-1) \), obtain the system response \( y(k) \) as a function of \( k \). (Note: \( u(k) \) is unit step function.)