% Sami Arica. March 24, 2014

% Plot of impulse and step response of the following LTI-causal system
% d^(2)/dt^(2) y(t) + 2 d/dt y(t) + 5 y(t) = x(t)
t = -1:0.01:10;
h = zeros(size(t));
s = zeros(size(t));
k = t > 0;
h(k) =  1/2 * exp(-t(k)) .* sin(2*t(k));
s(k) =  1/5 - 1/5 * exp(-t(k)) .* cos(2*t(k)) - 1/10 * exp(-t(k)) .* sin(2*t(k));

plot(t, h, 'k', 'LineWidth',2);
axis([-1, 10, -0.1 0.3])
text(3,0.15,'d^{2}/dt^{2} y(t) + 2 d/dt y(t) + 5 y(t) = x(t)',...
     'HorizontalAlignment','left')
xlabel('t [second]')
ylabel('h(t)')
title('The impulse response');
plot(t, s, 'k', 'LineWidth',2);
axis([-1, 10, -0.1 0.3])
text(3,0.1,'d^{2}/dt^{2} y(t) + 2 d/dt y(t) + 5 y(t) = x(t)',...
     'HorizontalAlignment','left')
xlabel('t [second]')
ylabel('s(t)')
title('The step response'); <!--'"</title></head>-->

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