Question $5$: The transfer function of a discrete$-$time system is given by

$H(z)=\frac{2z+1}{(z+1)(z+2)}$

$($a$)$ Analyze the stability of the system.

$(5$ marks$)$

$($b$)$ Find $h[n],$ the impulse response of the system.

$(5$ marks$)$

$($c$)$ Find $s[n],$ the step response of the system.

$(10$ marks$)$

Question $5$: The transfer function of a discrete$-$time system is given by

$H(z)=\frac{2z+1}{(z+1)(z+2)}$

$($a$)$ Analyze the stability of the system.

$(5$ marks$)$

$($b$)$ Find $h[n],$ the impulse response of the system.

$(5$ marks$)$

$($c$)$ Find $s[n],$ the step response of the system.

$(10$ marks$)$