Consider the system shown below:

Determine the difference equation of the overall system in terms of $\backslash$alpha and $\backslash$beta $.$ If $\backslash$alpha $=0\mathrm{.}5$ and $\backslash$beta $=$

$4,$ the difference equation is

y$[$n$]=2$x$[$n$]+4$x$[$n$-1]+(1)/(2)$y$[$n$-1]$

y$[$n$]=4$x$[$n$]+3$x$[$n$-1]+(1)/(2)$y$[$n$-1]$

y$[$n$]=2$x$[$n$]+(1)/(2)$x$[$n$-1]+4$y$[$n$-1]$

y$[$n$]=4$x$[$n$]+(1)/(2)$x$[$n$-1]+3$y$[$n$-1]$

Consider the interconnection of two LTI systems shown below

The impulse response of the first system is given as

h$\_(1)[$n$]=3(-(1)/(2))^($n$)$u$[$n$]-(-(1)/(2))^($n$-1)$u$[$n$-1]$

The second system is described by the difference equation

y$[$n$]=$w$[$n$]-(1)/(6)$y$[$n$-1]+(1)/(6)$y$[$n$-2]$

Find the frequency response of the overall system. From the frequency response, find the impulse

response. The value of the h$[3]$ is