Title: Applied Digital Signal Processing Author(s): Manolakis ISBN: 978052111002

Question

Title: Applied Digital Signal Processing
Author(s): Manolakis
ISBN: 9780521110020
>> You can readily find a free PDF download by Googling it.

Chapter: 6
Problem: 1
Parts: (a),(b),(c),(d)
>> If applicable, simply make use of a transform table as the basis of the solution.
>> Please write clearly.
>> For plot, just post the MATLAB code used to make plot.

1. Signal Xc(t) = 5 cos(2001+ + 4 sin(300 t) is sampled at a rate of Fs = 1 kHz to obtain the discrete-time signal x[n (a) Determine the spectrum X(ejo) of x[n] and plot its magnitude as a function of rad in Tam and as a function of F in Hz. Explain whether the original signal x(t) can be recovered from x[n]. (b) Repeat part (a) for F, 500 Hz. (c) Repeat part (a) for 100 Hz. (d) Comment on your results

Explanation / Answer

clear all
clc
%Question A ---------------------------------------------
t=[-5:10^-3:5]/1000;% This is t in seconds;
xt=exp(-1000*abs(t));
plot(t,xt);
figure
F=[-2:10^-3:2]*1000;
Xf=(0.002)./(1+(0.002.*pi.*F).^2);
plot(F,Xf);
%Question B ---------------------------------------------
figure
n=[-5:5];
Ts=1/1000;
xn1=exp(-1000*abs(n.*Ts));
stem(n*Ts,xn1);
figure
F=[-2:0.001:2]*1000;
for h=1:length(F)
Xnts=xn1.*exp(-1i.*2.*pi.*n.*Ts.*F(h));
Xef1(h)=sum(Xnts);
end
plot(F,Xef1);
%Question C ---------------------------------------------
figure
n=[-25:25];
Ts=1/5000;
xn2=exp(-1000*abs(n.*Ts));
stem(n*Ts,xn2);
figure
F=[-2:0.001:2]*1000;
for h=1:length(F)
Xnts=xn2.*exp(-1i.*2.*pi.*n.*Ts.*F(h));
Xef2(h)=sum(Xnts);
end
plot(F,Xef2);
%Question D ---------------------------------------------
figure
ts1=[-0.005:1/1000:0.005];
[G1,G2]=meshgrid(t,ts1);
S=sinc(1000*(G1-G2));
yr1=xn1*S;
plot(t,yr1)
figure
plot(t,yr1,t,xt)
%Question E ---------------------------------------------
figure
ts2=[-0.005:1/5000:0.005];
[G1,G2]=meshgrid(t,ts2);
S=sinc(5000*(G1-G2));
yr2=xn2*S;
plot(t,yr2)
figure
plot(t,yr2,t,xt)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.