Consider the LTI system with the difference equation

$y[n]=5y[n-1]-8y[n-2]+4y[n-3]+x[n]+x[n-1]+x[n-2]-4x[n-4]$

a$)$ Find the transfer function $H(z).$

b$)$ Write a Python code to print and plot the poles and zeros of $H(z).$

c$)$ Compute $h[n].$

Note: You can get the poles of $H(z)$ from the python code in step b$).$ The poles are integers, so do round$-$off the poles

returned by the python code to the nearest integer.

d$)$ Does the ROC of $h[n]$ include the unit circle?

please solve the following question. Also explain how its done in detail. thanks

also solve the coding question if possible. if not then please tell me in detail how to solve it manually so that i can understand and code it