Suppose we cascade a differentiator and a smoother. The equation for the differentiator is w$[$n$]=$ x$[$n$]$ x$[$n $1],$ where w$[$n$]$ is the output and x$[$n$]$ the input. The equation for the smoother is y$[$n$]=23$ y$[$n $1]+13$w$[$n$]$ where y$[$n$]$ is the output and w$[$n$]$ is the input. $($a$)$ Obtain the difference equation relating the input x$[$n$]$ to the output y$[$n$]$ of the whole system. $($b$)$ Determine the steady$-$state response y$[$n$]$ to an input x$[$n$]=$ u$[$n$]+$ sin$($n$/2)$u$[$n