% y(n)=(3/4)*y(n-1) + (1/6)*y(n-2) + x(n)+(1/2)*x(n-1)
clc;
clear all;
close all;

cit = [1, 0.5]
men = [1, -0.75, -1/6]
roots(men)
figure;
zplane(cit, men)
figure;
freqz(cit, men, 'whole')

z = roots(cit);
p = roots(men);
theta = pi/4;
r = 0.99;
new_zero_pair = [0;0];
new_pole_pair = [r*exp(1j*theta); r*exp(-1j*theta)];
filter_cit = poly(new_zero_pair)
filter_men = poly(new_pole_pair)
z_new = [z; new_zero_pair];
p_new = [p; new_pole_pair];
cit_new = poly(z_new)
men_new = poly(p_new) 
figure;
zplane(cit_new, men_new)
figure;
freqz(cit_new, men_new, 'whole')