Q$3)$ Consider a discrete$-$time Linear Time$-$Invariant $($LTI$)$ system with the following input$-$output relation:

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

where x$[$n$]$ is the input signal and y$[$n$]$ is the output signal.

Part A: Find the Impulse Response h$[$n$]$h$[$n$]$h$[$n$]$ of the System

$1.$ To find the impulse response, recall that the impulse response h$[$n$]$ is the output of the system when the input is the discrete$-$time unit impulse signal $[$n$].$

Determine the impulse response h$[$n$]$ of the system using the given input$-$output relation.

Part B: Find the Output for a Given Input Signal

$2.$ Given the input signal x$[$n$]=$$[$n$]+$$[$n$1],$ where $[$n$]$ is the unit impulse function, find the output signal y$[$n$]$ using the convolution sum.