Question

Please use MATLAB code to answer these questions

2-1 Generate a pulse function with a pulse width 1 second as an input function, x(t), and use the

same exponential decay function as impulse response function, h(t). Using MATLAB to

calculate the output of the system y(t).

2-2 Reduce the pulse width (such as 0.1 second) and repeat the question 2. Analyze the

difference.

2-3 Change the decay constant of h(t) (such as 1 and 3) and repeat the question 2. Analyze the

difference.

The input should be your own pick.

Answer 1

%matlab

Ts=0.001;
t=0:Ts:5;
Ton=1;
x=1.*(t<=Ton);
T=1;
h=exp(-t./T);
y=conv(x,h)./(2*length(t)-1);
plot(t,y(1:length(t)));
xlabel('t');
ylabel('y(t)');
title(['convolution with pulse width T_{ON} = ' num2str(Ton) ' decay constant \tau = ' num2str(T)]);

------------------

%matlab

Ts=0.001;
t=0:Ts:5;
Ton=0.1;
x=1.*(t<=Ton);
T=3;
h=exp(-t./T);
y=conv(x,h)./(2*length(t)-1);
plot(t,y(1:length(t)));
xlabel('t');
ylabel('y(t)');
title(['convolution with pulse width T_{ON} = ' num2str(Ton) ' decay constant \tau = ' num2str(T)]);

---------------------