Consider the open loop system described by

$y(k)-0\mathrm{.}8y(k-1)-0\mathrm{.}9y(k-2)+y(k-3)-0\mathrm{.}1y(k-4)=x(k)$

where $x(k)$ is the input and $y(k)$ is the output of the system. You need to

$($a$)$ Determine the pulse transfer function for the system

$($b$)$ Determine the stability of the system by the Jury test