Consider a causal and stable discrete time LTI system whose input $[]$ and output $[]$ are related by the

second order difference equation:

$[]+1$

$6[1]1$

$6[2]=[][1]$

a$.$ Determine the frequency response $()$ of the system.

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

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

$4)$

$[].$

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

$2$

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

$2$