Question

Question 3) Given a system with an impulse response of: h(t) = te-2t(U(t)-U(t-4)). Use MATLAB to compute the output of the system with an input of: x(t)-3(U(t -2)-U(t - 5)

Answer 1

Matlab code:

clc;
clear all;
close all;
syms t tau;
x = 3*(heaviside(t-2)-heaviside(t-5))
h = t*exp(-2*t)*(heaviside(t)-heaviside(t-4))
y=int(subs(x,tau)*subs(h,t-tau),tau,0,t)
figure(1);
ezplot(x,[0,10]);
title('Input signal for LTI system');
xlabel('t')
ylabel('x(t)')
grid;
figure(2);
ezplot(h);
title('LTI System impulse response');
xlabel('t')
ylabel('h(t)')
grid;
figure(3);
ezplot(y),grid;
title('output y(t)')

output:

x =

3*heaviside(t - 2) - 3*heaviside(t - 5)


h =

-t*exp(-2*t)*(heaviside(t - 4) - heaviside(t))


y =

heaviside(t - 9)*((27*exp(-8))/4 + (27*exp(10 - 2*t))/4 - (3*t*exp(10 - 2*t))/2) - heaviside(t - 6)*((27*exp(-8))/4 + (9*exp(4 - 2*t))/4 - (3*t*exp(4 - 2*t))/2) + heaviside(t - 2)*((9*exp(4 - 2*t))/4 - (3*t*exp(4 - 2*t))/2 + 3/4) - heaviside(t - 5)*((27*exp(10 - 2*t))/4 - (3*t*exp(10 - 2*t))/2 + 3/4)


Input signal for LTI system 3 2.5 1.5 0.5 10

LTI System impulse response 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0.5 1.5 2.5 3.5

output y(t) 0.8 0.7 0.6 0.5 0.4 0.3 0.1 5.5 4.5 5 3.5 2.5 3