Digital Signal Processing Using MATLAB: A Problem Solving Companion, Fourth [4th] Edition Ed (Instructor's Solution Manual) (Solutions)

672 Pages·2016·5.085 MB·English

by  Vinay K. Ingle

An Instructor’s Solutions Manual to Accompany

DIGITAL SIGNAL PROCESSING USING
MATLAB, 4TH E
DITION

VINAY K. INGLE
JOHN G. PROAKIS
© 2017, 2012 Cengage Learning ISBN: 978-1-305-66781-5

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Instructor's Solutions Manual

to Accompany

Digital Signal Processing
using MATLAB

4th EDITION, I E
NTERNATIONAL DITION

VINAY K. PROAKIS

JOHN G. PROAKIS
Contents
2 Discrete-TimeSignalsandSystems 1
3 Discrete-TimeFourierTransform 55
4 The´-Transform 129
5 TheDiscrete-TimeFourierTransform 179
6 DigitalFilterStructures 259
7 FIRFilterDesign 337
8 IIRFilterDesign 415
9 Sampling-RateConversion 499
10 FiniteWord-LengthEffects 613
3
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Chapter 2
Discrete-Time Signals and Systems
P2.1 Generate the following sequences using the basic MATLAB signal functions and the basic MATLAB signal operations
discussedinthischapter. Plotsignalsamplesusingthestemfunction.
1. x .n/D3ı.nC2/C2ı.n/(cid:0)ı.n(cid:0)3/C5ı.n(cid:0)7/,(cid:0)5(cid:20)n(cid:20)15
1
% P0201a: x1(n) = 3*delta(n + 2) + 2*delta(n) - delta(n - 3) +
% 5*delta(n - 7), -5 <= n <= 15.
clc; close all;
x1 = 3*impseq(-2,-5,15) + 2*impseq(0,-5,15) - impseq(3,-5,15) + 5*impseq(7,-5,15);
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201a’); n1 = [-5:15];
Hs = stem(n1,x1,’filled’); set(Hs,’markersize’,2);
axis([min(n1)-1,max(n1)+1,min(x1)-1,max(x1)+1]);
xlabel(’n’,’FontSize’,LFS); ylabel(’x_1(n)’,’FontSize’,LFS);
title(’Sequence x_1(n)’,’FontSize’,TFS);
set(gca,’XTickMode’,’manual’,’XTick’,n1,’FontSize’,8);
print -deps2 ../EPSFILES/P0201a;
Theplotsofx .n/isshowninFigure2.1.
1
Sequence x (n)
1
6
5
4
3
)
n
( 2
1
x
1
0
(cid:239)1
(cid:239)2
(cid:239)5 (cid:239)4 (cid:239)3 (cid:239)2 (cid:239)1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n
Figure2.1: ProblemP2.1.1sequenceplot
1
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2 SOLUTIONSMANUALFORDSPUSINGMATLAB(4THEDITION)
5
2. x .n/D X e(cid:0)jkjı.n(cid:0)2k/,(cid:0)10(cid:20)n(cid:20)10.
2
kD(cid:0)5
% P0201b: x2(n) = sum_{k = -5}^{5} e^{-|k|}*delta(n - 2k), -10 <= n <= 10
clc; close all;
n2 = [-10:10]; x2 = zeros(1,length(n2));
for k = -5:5
x2 = x2 + exp(-abs(k))*impseq(2*k ,-10,10);
end
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201b’);
Hs = stem(n2,x2,’filled’); set(Hs,’markersize’,2);
axis([min(n2)-1,max(n2)+1,min(x2)-1,max(x2)+1]);
xlabel(’n’,’FontSize’,LFS); ylabel(’x_2(n)’,’FontSize’,LFS);
title(’Sequence x_2(n)’,’FontSize’,TFS);
set(gca,’XTickMode’,’manual’,’XTick’,n2);
print -deps2 ../EPSFILES/P0201b;
Theplotsofx .n/isshowninFigure2.2.
2
Sequence x (n)
2
2
1.5
1
)
n
( 0.5
2
x
0
−0.5
−1
−10−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10
n
Figure2.2: ProblemP2.1.2sequenceplot
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
SOLUTIONSMANUALFORDSPUSINGMATLAB(4THEDITION) 3
3. x .n/D10u.n/(cid:0)5u.n(cid:0)5/(cid:0)10u.n(cid:0)10/C5u.n(cid:0)15/.
3
% P0201c: x3(n) = 10u(n) - 5u(n - 5) + 10u(n - 10) + 5u(n - 15).
clc; close all;
x3 = 10*stepseq(0,0,20) - 5*stepseq(5,0,20) - 10*stepseq(10,0,20) ...
+ 5*stepseq(15,0,20);
n3 = [0:20];
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201c’);
Hs = stem(n3,x3,’filled’); set(Hs,’markersize’,2);
axis([min(n3)-1,max(n3)+1,min(x3)-1,max(x3)+2]);
ytick = [-6:2:12];
xlabel(’n’,’FontSize’,LFS); ylabel(’x_3(n)’,’FontSize’,LFS);
title(’Sequence x_3(n)’,’FontSize’,TFS);
set(gca,’XTickMode’,’manual’,’XTick’,n3);
set(gca,’YTickMode’,’manual’,’YTick’,ytick);
print -deps2 ../EPSFILES/P0201c;
Theplotsofx .n/isshowninFigure2.3.
3
Sequence x (n)
3
12
10
8
6
) 4
n
(
3
x 2
0
−2
−4
−6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
n
Figure2.3: ProblemP2.1.3sequenceplot
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4 SOLUTIONSMANUALFORDSPUSINGMATLAB(4THEDITION)
4. x .n/De0:1nŒu.nC20/(cid:0)u.n(cid:0)10/(cid:141).
4
% P0201d: x4(n) = e ^ {0.1n} [u(n + 20) - u(n - 10)].
clc; close all;
n4 = [-25:15];
x4 = exp(0.1*n4).*(stepseq(-20,-25,15) - stepseq(10,-25,15));
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201d’);
Hs = stem(n4,x4,’filled’); set(Hs,’markersize’,2);
axis([min(n4)-2,max(n4)+2,min(x4)-1,max(x4)+1]);
xlabel(’n’,’FontSize’,LFS); ylabel(’x_4(n)’,’FontSize’,LFS);
title(’Sequence x_4(n)’,’FontSize’,TFS); ntick = [n4(1):5:n4(end)];
set(gca,’XTickMode’,’manual’,’XTick’,ntick);
print -deps2 ../CHAP2_EPSFILES/P0201d; print -deps2 ../../Latex/P0201d;
Theplotsofx .n/isshowninFigure2.4.
4
Sequence x (n)
4
3
2.5
2
) 1.5
n
(
4
x 1
0.5
0
−0.5
−1
−25 −20 −15 −10 −5 0 5 10 15
n
Figure2.4: ProblemP2.1.4sequenceplot
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
SOLUTIONSMANUALFORDSPUSINGMATLAB(4THEDITION) 5
5. x .n/D5Œcos.0:49(cid:25)n/Ccos.0:51(cid:25)n/(cid:141); (cid:0)200(cid:20)n(cid:20)200. Commentonthewaveformshape.
5
% P0201e: x5(n) = 5[cos(0.49*pi*n) + cos(0.51*pi*n)], -200 <= n <= 200.
clc; close all;
n5 = [-200:200]; x5 = 5*(cos(0.49*pi*n5) + cos(0.51*pi*n5));
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201e’);
Hs = stem(n5,x5,’filled’); set(Hs,’markersize’,2);
axis([min(n5)-10,max(n5)+10,min(x5)-2,max(x5)+2]);
xlabel(’n’,’FontSize’,LFS); ylabel(’x_5(n)’,’FOntSize’,LFS);
title(’Sequence x_5(n)’,’FontSize’,TFS);
ntick = [n5(1): 40:n5(end)]; ytick = [-12 -10:5:10 12];
set(gca,’XTickMode’,’manual’,’XTick’,ntick);
set(gca,’YTickMode’,’manual’,’YTick’,ytick);
print -deps2 ../CHAP2_EPSFILES/P0201e; print -deps2 ../../Latex/P0201e;
Theplotsofx .n/isshowninFigure2.5.
5
Sequence x (n)
5
12
10
5
)
n
( 0
5
x
−5
−10
−12
−200 −160 −120 −80 −40 0 40 80 120 160 200
n
Figure2.5: ProblemP2.1.5sequenceplot
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
6 SOLUTIONSMANUALFORDSPUSINGMATLAB(4THEDITION)
6. x .n/D2sin.0:01(cid:25)n/cos.0:5(cid:25)n/; (cid:0)200(cid:20)n(cid:20)200.
6
%P0201f: x6(n) = 2 sin(0.01*pi*n) cos(0.5*pi*n), -200 <= n <= 200.
clc; close all;
n6 = [-200:200]; x6 = 2*sin(0.01*pi*n6).*cos(0.5*pi*n6);
Hf_1 = figure; set(Hf_1,’NumberTitle’,’off’,’Name’,’P0201f’);
Hs = stem(n6,x6,’filled’); set(Hs,’markersize’,2);
axis([min(n6)-10,max(n6)+10,min(x6)-1,max(x6)+1]);
xlabel(’n’,’FontSize’,LFS); ylabel(’x_6(n)’,’FontSize’,LFS);
title(’Sequence x_6(n)’,’FontSize’,TFS);
ntick = [n6(1): 40:n6(end)];
set(gca,’XTickMode’,’manual’,’XTick’,ntick);
print -deps2 ../CHAP2_EPSFILES/P0201f; print -deps2 ../../Latex/P0201f;
Theplotsofx .n/isshowninFigure2.6.
6
Sequence x (n)
6
3
2
1
)
n
( 0
6
x
−1
−2
−3
−200 −160 −120 −80 −40 0 40 80 120 160 200
n
Figure2.6: ProblemP2.1.6sequenceplot
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.