The difference equation for a process model with a zero$-$order hold can be

written:

$y(k)=0\mathrm{.}125u(k-1)+0\mathrm{.}102u(k-2)+1\mathrm{.}489y(k-1)-0\mathrm{.}549y(k-2)$

Where $u(k)$ and $y(k)$ are respectively the input signal and the output signal.

a$.$ What is the process pulse transfer function $Y\frac{z}{U}(z).$

b$.$ Use simulation method or $($optional$)$ long division, to find the time response $y(k)$ to

unit step change in $u(k)$ for the first $5$ samples.

c$.$ What is the steady state value of $y(k)$ if $u(k)$ is a unit step change?