% Matlab example of lecture convolution example 
% 
% x(t) = exp(-a t) u(t);
% y(t) = r(t);
%

a = 4;

del_t = .001;
tx = 0:del_t:10;
th = 0:del_t:20;
Lx= length(tx);
Lh= length(th);
tp = [(tx(1)+th(1)):del_t:(tx(Lx)+th(Lh))];
Lp = length(tp);

x = exp(-a .* tx) .* stp_fn(tx);
h = rmp_fn(th);
ye = ((1/a) .* rmp_fn(tp)) - (1/(a*a)) .* (1 - exp(-a .* tp));

y = del_t * conv(x,h);  % Multiply by step size to approximate
                        % rectangular rule integration.

figure(3)
subplot(3,1,1), plot(tx,x,'LineWidth',6), xlabel('t'), ylabel('x(t)');
title('x(t)');
subplot(3,1,2), plot(th,h,'LineWidth',6), xlabel('t'), ylabel('h(t)');
title('h(t)');
subplot(3,1,3), plot(tp,y,'r','LineWidth',16);
hold on;
plot(tp,ye,'b','LineWidth',12), xlabel('t'), ylabel('y(t){r} & y[t]{b}');
title('y(t) = x(t) * h(t) \{comp. red\} \{hand blue\}');
hold off;

figure(4)
subplot(4,1,1),plot(tp,(y-ye),'r','LineWidth',6);
axis([tp(1) (th(Lh)- tx(Lx)) -.001 .04])
title('error primarily due to truncation of x(t)');
subplot(4,1,3),plot(tp,(y-ye),'r','LineWidth',6);
axis([(th(Lh)-1) (th(Lh)+tx(Lx)) -10 0.1])
title('error primarily due to truncation of h(t)');

tx = 0:del_t:1;
th = 0:del_t:10;
Lx= length(tx);
Lh= length(th);
tp = [(tx(1)+th(1)):del_t:(tx(Lx)+th(Lh))];
Lp = length(tp);

x = exp(-a .* tx) .* stp_fn(tx);
h = rmp_fn(th);
ye = ((1/a) .* rmp_fn(tp)) - (1/(a*a)) .* (1 - exp(-a .* tp));

y = del_t * conv(x,h);  % Multiply by step size to approximate
                        % rectangular rule integration.

figure(3)
subplot(3,1,1), hold on
plot(tx,x,'g','LineWidth',2), xlabel('t'), ylabel('x(t)');
title('x(t)');
hold off
subplot(3,1,2), hold on
plot(th,h,'g','LineWidth',2), xlabel('t'), ylabel('h(t)');
title('h(t)');
hold off
subplot(3,1,3), hold on
plot(tp,y,'g','LineWidth',6);
plot(tp,ye,'y','LineWidth',4), xlabel('t'), ylabel('y(t){g} & y[t]{y}');
title('y(t) = x(t) * h(t) \{comp. red\} \{hand blue\} \{comp. green\} \{hand yellow\} ');
hold off

figure(4)
subplot(4,1,2)
plot(tp,(y-ye),'g','LineWidth',3);
axis([tp(1) (th(Lh)- tx(Lx)) -.04 .005])
title('error primarily due to truncation of x(t)');
subplot(4,1,4)
plot(tp,(y-ye),'g','LineWidth',3);
axis([(th(Lh)-1) (th(Lh)+tx(Lx)) -5 .1])
title('error primarily due to truncation of h(t)');