Question

Exercise 2: Fourier Transform properties (a) Time Scaling. Create an M-file and: 1. Plot the waveform s(t)sinc(at/0.5) where a1 and t fro5 tot4.99 (seconds) in 0.01 increments. 2. Plot the amplitude spectrum of s(t). Comment the figure. 3. Repeat (a.1) and (a.2) for α-2. How do this signals compare in tune? How do their bandwidths compare? (b) Time Shifting. Create an M-file and: 1. Plot s(t)rectpuls(t) and s2(t)rectpuls(t 2.5), where t is in the range t =-5 to t = 4.95 (seconds) with increment of 0.05. 2. Plot the amplitude spectrum of si() and s2(t). How do they compare? NOTE: The function rectpuls is available in MATLAB. Type help rectpuls for more information (e) Modulation Theorem Create an M-file and: I. Plot the pulse s(t) = sinc(t), where t is in the range fron t =-5 to t = 4.99 (seconds) using incremnt of 0.01 2. Plot the amplitude spectrum of s(t) 3. Plot the signal sm(t) s(tcos(2m Jet) for fe-10 Hz 4. Plot the amplitude spectrum of sm(t) for fe = 10 Hz. Compare the spectrum of this signal with the spectrum you obtained in (c.2).

help with this matlab problem asap thank you....

Answer 1

%%
%a
t=-5:.01:4.99;
alpha=1;
s=.5*sin(alpha*t)./t;
figure
plot(t,s)
title(['Time scaling: s(t) for \alpha = ',num2str(alpha)])
figure
plot(t,abs(s))
title(['Time scaling: amplitude spectrum of s(t) for \alpha = ',num2str(alpha)])
alpha=2;
s=.5*sin(alpha*t)./t;
figure
plot(t,s)
title(['Time scaling: s(t) for \alpha = ',num2str(alpha)])
figure
plot(t,abs(s))
title(['Time scaling: amplitude spectrum of s(t) for \alpha = ',num2str(alpha)])

%%
%b
t=-5:.05:4.95;
s1=rectpuls(t);
s2=rectpuls(t-2.5);
figure
plot(t,s1,t,s2)
legend('s_1(t)','s_2(t)')
title('Time shifting: s_1(t) and s_2(t)')
figure
plot(t,abs(s1),t,abs(s2))
legend('s_1(t)','s_2(t)')
title('Time shifting: amplitude spectrum')

%%
%c
t=-5:.01:4.99;
s=sin(t)./t;
figure
plot(t,s)
title('Modulation Theorem: s(t)')
figure
plot(t,abs(s))
title('Modulation Theorem: amplitude spectrum of s(t)')
sm=s.*cos(2*pi*10*t);
figure
plot(t,sm)
title('Modulation Theorem: s_m(t)')
figure
plot(t,abs(sm))
title('Modulation Theorem: amplitude spectrum of s_m(t)')