6.a)
function Problem y=f(t)
%This function computes the value of -t(u(t+1)-u(t))
y=-t.*((t+1>=0)-(t>=0));
Problem 6.b)
t= -4:.01:4;
subplot(3,2,1)
plot(t,f(t))
title($f(t)$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 3/2])
subplot(3,2,2)
plot(t,f(-t))
title($f_1(t)=f(-t)$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 3/2])
subplot(3,2,3)
plot(t,f(t-1)+f(1-t))
title($f_2(t) = f(t-1) + f(1-t)$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 5/2])
subplot(3,2,4)
plot(t,f(t-1)+f(-t-1))
title($f_3(t) = f(t-1)+f(-t-1)$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 5/2])
subplot(3,2,5)
plot(t,f(t-1/2)+f(-(t+1/2)))
title($f_4(t) = f(t-1/2)+f(-(t+1/2))$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 3/2])
subplot(3,2,6)
plot(t, 3/2*f(t/2-1) )
title($f_5(t) = 3/2f(t/2-1)$,interpreter,latex,fontsize,14)
grid on
ylim([-1/2 2])
Problem 6.c)
t = -4:.01:4;
z=0.01*conv(f(t),f(t));
figure
plot(-8:0.01:8,z)
title($z(t)=f(t) * f(t)$,interpreter,latex,fontsize,14)
grid on
1
Problem 6.d)
function question6d
% convolves and plots two and three pulses, respectively.
figure;
% convolve two pulses
t = -4:.01:4;
[tp y] = conv_pulses(t, 2);
% plot two pulses
subplot(2,1,1)
plot(tp,y)
title($z(t)=p(t) convolved * p(t)$,interpreter,latex,fontsize,14)
xlim([t(1) t(end)])
grid on
% convolve three pulses
t = -4:.01:4;
[tp y] = conv_pulses(t, 3);
% plot three convolved pulses
subplot(2,1,2)
plot(tp,y)
title($z(t)=p(t) * p(t) * p(t)$,interpreter,latex,fontsize,14)
xlim([t(1) t(end)])
grid on
end
function [tp y] = conv_pulses(t, n)
% convolves n pulses together. pulses defined by p(t)
dt = t(2)-t(1);
y = p(t);
for i = 1:n-1
y = conv(y,p(t))*dt;
end
tp = n*t(1):.01:n*t(end);
end
function z = p(t)
% definition of pulse
z = f( (t-1)/2 ) + f( -(t+1)/2 );
end
2
f (t)
f1 (t) = f (t)
1.5
1.5
1
1
0.5
0.5
0
0
0.5
4
2
0
2
4
0.5
4
f2 (t) = f (t 1) + f (1 t)
2
0
2
4
f3 (t) = f (t 1) + f (t 1)
2
2
1
1
0
0
4
2
0
2
4
4
f4 (t) = f (t 1 / 2) + f ((t + 1 / 2))
2
0
2
4
f5 (t) = 3 / 2 f (t/ 2 1)
1.5
2
1
1.5
1
0.5
0.5
0
0.5
4
0
2
0
2
4
0.5
4
2
0
2
4
z (t) = f (t) f (t)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
8
6
4
2
0
2
4
6
8
z (t) = p (t) p (t)
2.5
2
1.5
1
0.5
0
4
3
2
1
0
1
2
3
4
2
3
4
z (t) = p (t) p (t) p (t)
4
3
2
1
0
4
3
2
1
0
1