%%Part 1 Commutative

T=0.1;
t1=-2:T:-1-T;
t2=-1:T:0;t3=T:T:1;
t4=1+T:T:2;
t=[t1 t2 t3 t4];
tf1=[t2 t3];
tf2=[t2 t3];
f1=[ones(1,11) ones(1,10)];
f2=[t2+1 1-t3];
f12=T*conv(f1,f2);
f21=T*conv(f2,f1);

figure(1)
plot(t, f12)
grid on;
title('Commutative')
ylabel('pulse(t)*triangle(t)')
xlabel('Time t')

figure(2)
plot(t, f21)
grid on;
title('Commutative')
ylabel('triangle(t)*pulse(t)')
xlabel('Time t')

figure(3)
plot(tf1, f1)
grid on;
title('Pulse')
ylabel('pulse(t)')
xlabel('Time t')
axis([-1.1 1.1 0 1.1]);

figure(4)
plot(tf2, f2)
grid on;
title('Triangle')
ylabel('triangle(t)')
xlabel('Time t')

%%Part 2
%%a)
%%

num=[1 5];
den=[1 4 3];
t=0:0.1:5;
h=impulse(num,den,t);
figure(5)
plot(t,h)
grid on;
title('Impulse of function')
ylabel('H(s)')
xlabel('Time t')
%%B)

f=ones(1,length(t));
t=0:0.1:10;
figure(6);
plot(t, conv(f,h))
grid on;
title('Step Response')
ylabel('Conv(f,h)')
xlabel('Time t')

%%C)
t=0:0.1:5;
f=sin(2*t);
t=0:0.1:10;
figure(7);
plot(t,conv(f,h))
grid on;
title('System zero-state response using sin(2t)')
ylabel('conv(sin(2t),h)')
xlabel('Time t')