% 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');

x = [zeros(1, 10), 1, zeros(1, 100)]
y = zeros(size(x));
for n = 3:length(x)
    y(n) = 0.75*y(n-1) + (1/6)*y(n-2) + x(n) + 0.5*x(n-1)

    stem(0:length(x)-1, y, 'filled');     % plot discrete-time sequence
    title(['System output up to sample n = ' num2str(n)]);
    xlabel('n');
    ylabel('y(n)');
    ylim([-0.5 1.5]);                     % fixed axis for stability
    grid on;
    pause(0.25);
end