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: 3
Parts: (a),(b),(c),(d)
>> If applicable, simply make use of a transform table as the basis of the solution.
>> Please write clearly.
>> For graphs, just post the MATLAB code used to make graphs.

3. Consider a continuous-time signal Xo (t) = 2 cos(101-60°)-3 sin( 16). It is sampled at t = 0.05n to obtain x[n] which is then applied to an ideal DAC to obtain another continuous-time signal yr(t) (a) Determine x[n] and graph its samples along with the signal xc(t) in one plot. (b) Determine yr (t) as a sinusoidal signal. Graph and compare it with xc(t). (c) Repeat (a) and (b) for sampling at t = 0.1 . Comment on your results (d) Repeat (a) and (b) for sampling at 0.5n. 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)

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