Write a MATLAB program to plot the solution to the three difference equations in Exercise 1.18 for \(\omega=\pi / 3\) and \(\omega=\pi\).

Exercise 1.18

Determine the steady-state response for the input \(x(n)=\sin (\omega n) u(n)\) of the filters described by

(a) \(y(n)=x(n-2)+x(n-1)+x(n)\)

(b) \(y(n)-\frac{1}{2} y(n-1)=x(n)\)

(c) \(y(n)=x(n-2)+2 x(n-1)+x(n)\).

What are the amplitude and phase of \(y(n)\) as a function of \(\omega\) in each case?