Notes

% Define the system H1 and H2 as transfer functions using the given difference equations

% H1: y1[n] = 0.5y1[n-1] + x[n]
% Transfer function H1
a1 = [1 -0.5]; % Coefficients for y1
b1 = [1]; % Coefficients for x

% H2: y2[n] = 0.7y2[n-1] - 0.1y2[n-2] + x2[n] - 0.5x2[n-1]
% Transfer function H2
a2 = [1 -0.7 0.1]; % Coefficients for y2
b2 = [1 -0.5]; % Coefficients for x2

% Combine the two systems in cascade (series connection)
sys1 = tf(b1, a1, -1); % H1 transfer function
sys2 = tf(b2, a2, -1); % H2 transfer function
sys_total = series(sys1, sys2); % Overall system

% Compute and plot the impulse response
figure;
impulse(sys_total);
title('Impulse Response of the Entire System');
grid on;





% Define the input signal x1[n] = cos(0.2*pi*n)
n = 0:100; % Time indices
x1 = cos(0.2*pi*n); % Input signal

% Simulate the system output to input x1
[y, t] = lsim(sys_total, x1, n);

% Plot the output
figure;
plot(n, y);
title('System Response to x1[n] = cos(0.2*pi*n)');
xlabel('n');
ylabel('Output');
grid o