$($a$)$ Given a discrete$-$time signal x$($n$)$ with the z$-$transform X$($z$)=20\mathrm{.}08551\mathrm{.}0043$z$1+0\mathrm{.}8034$z$2+9\mathrm{.}6411$z$3.$ Determine and plot x$($n$).$ What is the length of the signal? Consider the signal y$($n$)$ with Y $($z$)=$ log$($X$($z$)),$ where y$($n$)$ is the inverse z$-$transform of Y$($z$).$ Expand Y$($z$)$ in a power series and then determine and plot y$($n$).$ Hint:. Retain only the most significant terms in the series