% Program P2_6
% Cascade Realization
clf;
x = [1 zeros(1,40)]; % Generate the input
n = 0:40;
% Coefficients of 4th order system
den = [1 1.6 2.28 1.325 0.68];
num = [0.06 -0.19 0.27 -0.26 0.12];
% Compute the output of 4th order system
y = filter(num,den,x);
% Coefficients of the two 2nd order systems
num1 = [0.3 -0.2 0.4];den1 = [1 0.9 0.8];
num2 = [0.2 -0.5 0.3];den2 = [1 0.7 0.85];
% Output y1[n] of the first stage in the cascade
y1 = filter(num1,den1,x);
% Output y2[n] of the second stage in the cascade
y2 = filter(num2,den2,y1);
% Difference between y[n] and y2[n]
d = y - y2;
% Plot output and difference signals
subplot(3,1,1);
stem(n,y);
ylabel('Amplitude');
title('Output of 4th order Realization'); grid;
subplot(3,1,2);
stem(n,y2)
ylabel('Amplitude');
title('Output of Cascade Realization'); grid;
subplot(3,1,3);
stem(n,d)
xlabel('Time index n');ylabel('Amplitude');
title('Difference Signal'); grid;