Consider a causal LTI system described by the difference equation

y$[$n$]+1$

$2$

y$[$n $1]=$ x$[$n$](1)$

$1.$ Determine the frequency response H$($e

j$)$ of this system

$2.$ What is the response of the system to the following inputs?

$($a$)$ x$[$n$]=(1/2)$nu$[$n$]$

$($b$)$ x$[$n$]=$ $[$n$]+1/2$$[$n $1]$