$y[n]=-{\displaystyle \underset{k=0}{\overset{N-1}{}}}{a}_{k}y[n-N+k]+{\displaystyle \underset{k=0}{\overset{M-1}{}}}{b}_{k}x[n-M+k]$

$a_0=0\mathrm{.}819,a_1=-1\mathrm{.}783,b_0=0\mathrm{.}017,b_1=0\mathrm{.}019,M=N=2$

A second$-$order discrete system defined by the following difference

equation is considered.

a$)$ Write the explicit expression of the difference equation.

b$)$ Using the difference equation, develop a program that calculates

and plots the first $100$ values of the output signal if the input signal is

applied to the system step by step at time $n=1$ for $y[0]=y[1]=0.$

c$)$ Send the program you developed in $($b$)$ to the user.

$M,N,a0,a1,...,aN-1,b0,b1,...,bM-1,y[0],y[1],...,y[N-1]$

Generalize it to a program that takes values as input and calculates

and plots the output signal for the input signal unit step by unit.