$13\mathrm{.}15$ Given the difference equation

$1$

y$[$k$]+$y$[$k$-1]+-$y$[$k$-2]=$x$[$k$]-$x$[$k$-2],$

$($i$)$ determine the transfer function representing the LTID system;

$($ii$)$ determine the impulse response of the LTID system;