Consider a causal system for which the input $x[n]$ and the output $y[n]$ are related by the linear constant coefficient difference equation below

$[100\%]$

$y[n]=x[n]+x[n-4]$

a$)$ Determine the unit sample response of the system.

$[20\%]$

b$)$ Calculate the frequency response of the system and plot the magnitude response.

$[40\%]$

c$)$ Determine the system response to the input of

$x[n]=cos(\frac{}{2}n)+cos(\frac{}{4}n),-$

using discrete$-$time Fourier transform.

$[20\%]$

$d$