2) Let xc(t) and xs(t) be the continuous-time signals Xc(t) = sin(50 pi t)cos(25

Question

2) Let xc(t) and xs(t) be the continuous-time signals Xc(t) = sin(50 pi t)cos(25 pi t)/pi Xs(t) = Sigma^infinity n = -infinity xc(t) delta (t ? n/100) a) Use MATLAB to plot xc(t). b) Find and plot the Fourier transform xc(w) of xc(t). c) Find and plot the Fourier transform xs(w) of xs(t). d) Plot the frequency response of the continuous-time lowpass filter with the smallest width in frequency that will recover xc(t) from xs(t). e) Plot the frequency response of the continuous-time lowpass filter with the largest width in frequency that will recover xc(t) from xs(t).

Explanation / Answer

clc;
clear all;
close all;
t=-100:.1:100;
Xc=sin(50*pi*t).*cos(25*pi*t)./(pi*t)
Xs=0;
for n=-100:100
Xs=Xs+Xc.*dirac(t-n/100);
end
figure(1)
subplot(1,2,1)
plot(t,Xc,'b')
grid on;
title('continuous time signal sin(50*pi*t).*cos(25*pi*t)./(pi*t)')
xlabel('time -->')
ylabel('amplitude -->')
[Xc_w,w1]=fft(Xc,t);
subplot(1,2,2)
plot(w1,Xc_w,'b')
grid on;
title('continuous spectrum of sin(50*pi*t).*cos(25*pi*t)./(pi*t)')
xlabel('angular frequency -->')
ylabel('amplitude -->')
figure(2)
subplot('1,2,1')
plot(t,Xs,'b')
title('continuous time signal ')
xlabel('time -->')
ylabel('amplitude -->')
[Xs_w,w2]=fft(Xw,t);
subplot(1,2,2)
plot(w2,Xs_w,'b')
grid on;
title('continuous time signal sin(50*pi*t).*cos(25*pi*t)./(pi*t)')
xlabel('time -->')
ylabel('amplitude -->')

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