Consider a discrete$-$time LTI system with impulse response h$[$n$]$ given by

h$[$n$]=3((1)/(3))^($n$)$u$[$n$]$

Using DTFT find the output, y$[$n$]$ of the system to an input x$[$n$]=($n$+1)((1)/(2))^($n$)$u$[$n$].$ The value

of y$[1]$ is

Consider a discrete$-$time LTI system with impulse response h$[$n$]$ given by

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

Using DTFT find the output, y$[$n$]$ of the system to an input x$[$n$]=(-1)^($n$).$ The value of y$[1]$ is

Consider the interconnection of two LTI systems shown below

The impulse response of the first system is given as

h$\_(1)[$n$]=($sin$(0\mathrm{.}5\backslash$pi n$))/(\backslash$pi n$)$

System $2$ is described by the difference equation

y$[$n$]=$w$[$n$]-$w$[$n$-1]$

The input applied to the system is

x$[$n$]=$cos$((3\backslash$pi $)/(4)$n$)+6\backslash$pi $\backslash$delta $[$n$-2]+5$

Determine the output of the overall system, y$[$n$].$ The value of y$[5]$ is