Question

Please show using MATLAB Answer

7. Obtain the convolution of the pairs of signals in Figure 7 h(t) a(t) 0 2 h(t) r(t) 0 0 Figure 7: Signal pairs Therefore, y(t) = 0 otherwise

Answer 1

MATLAB:

1)

clc;close all;clear all;
t=0:0.001:2
x=(t>=0 &t<=1)
h=(t>=0 &t<=1)+(-1*(t>=1 &t<=2))
t1=0:0.001:4
y=conv(x,h)
figure(1)
subplot(311)
plot(t,x,'b','linewidth',3)
title('Input x(t)')
xlabel('t');ylabel('x(t)')
xlim([0,4]);ylim([-1,1])

subplot(312)
plot(t,h,'m','linewidth',3)
title('Impulse response h(t)')
xlabel('t');ylabel('h(t)');xlim([0,4])

subplot(313)
plot(t1,y/max(y),'r','linewidth',3)
title('Output y(t)')
xlabel('t');ylabel('y(t)');xlim([0,4])

figure(2)
%verify with the given answer
t=0:0.01:5
y=(t.*(t>=0 &t<1))+((3-(2*t)).*(t>=1 & t<2))+((t-3).*(t>=2 &t<=3))
plot(t,y,'r','linewidth',3)
title('Output y(t)')
xlabel('t');ylabel('y(t)');

Input x(t) 0.5 0.5 2 3 4 Impulse response h(t) 0.5 0.5 2 3 4 Output y(t) 0.5 -0.5 2 3 4

Output y(t) 0.5 0.5

2)

clc;close all;clear all;
t=0:0.001:6
x=t.*(t>=0 &t<=1)
h=(t>=2 &t<=5)
t1=0:0.001:12
y=conv(x,h)
subplot(311)
plot(t,x,'b','linewidth',3)
title('Input x(t)')
xlabel('t');ylabel('x(t)')
ylim([0,2]);xlim([0,2])

subplot(312)
plot(t,h,'m','linewidth',3)
title('Impulse response h(t)')
xlabel('t');ylabel('h(t)');
ylim([0,2]);xlim([0,6])

subplot(313)
plot(t1,y/max(y),'r','linewidth',3)
title('Output y(t)')
xlabel('t');ylabel('y(t)');
ylim([0,2])

Input x(t) 1.5 0.5 0.5 1.5 2 Impulse response h(t) 1.5 0.5 3 4 6 Output y(t) 2 1.5 F 'ג1 0.5 10 2 4 8 12