Problem $5$ Consider a causal and stable discrete time LTI system whose input x$[$n$]$ and output y$[$n$]$ are related by the

second order difference equation:

$1$

$1$

y$[$n$]+$ y$[$n $-1]-$ y$[$n $-2]=$ x$[$n$]-$ x$[$n $-1]$

$6$

$6$

a$.$ Determine the frequency response $($e j$\backslash$Omega $)$ of the system.

b$.$ Determine the impulse response of the system, h$[$n$].$

$1$ n

c$.$ Determine the response of the system,$1[],$ to an input $1[]=()[].$

$4$

$$

d$.$ Determine the response of the system, $2[],$ to an input $2[]=22$

$$

e$.$ Determine the response of the system, $3[],$ to an input $3[]=2$ cos $().$