Consider the following LTI filter:

$H(z)=\frac{1-0\mathrm{.}3z^{-1}}{1-0\mathrm{.}7z^{-1}+0\mathrm{.}1z^{-2}}$

$($a$)$ Find the poles and zeros of $H(z).$

$($b$)$ Sketch the pole$-$zero plot and show all possibilities of ROC. Is this system stable? Justify.

$($c$)$ If the system is causal. Find the impulse response $h(n)$ of this system.

$($d$)$ Develop a Direct Form II realization of this filter.

$($e$)$ Develop a parallel realization with two first$-$order sections.

$($f$)$ If the system is causal. Find the output $y(n)$ if the input $x(n)=(0\mathrm{.}3{)}^{n-1}u(n-2).$