When the input to an LTI system is

$][$

$4$

$1$

$][$ nunx

n

$$

$$

$$

$$

$$

$$

$$

the output is

$][$

$4$

$1$

$][$

$2$

$1$

$2][$ nununy

nn

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

a$)$ Find the system function H$($z$)$ of the system

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

c$)$ Write the difference equation that characterizes the system

d$)$ Is the system stable?