Worksheet22201.docx
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Worksheet22201
MatlabWorksheet2
PartA（In-classroomexercises）
1.Usingplottodisplaythefollowingvoltagewithappropriatelinetype,titleandlabels.Alsopresentthegraphwithsuitablerangesofaxis.
wheref=50Hz.
（Hint:
timeintervalmustbesmallenough,e.g.0.001seconds.Therefore,t=0:
0.001:
1isappropriate）;
ANSWER:
t=0:
0.001:
1;
v=220*sin（2*pi*50*t）;
plot（t,v）;
2.Usingplottodisplaythefollowingvoltagewithappropriatelinetype,titleandlabels.Alsopresentthegraphwithsuitablerangesofaxis.
wheref=50Hz.
Inaddition,onthesamegraph,drawtheenvelopeoftheoscillationandaddlegends.
ANSWER:
v2=220.*exp（-5.*t）.*sin（2*pi*50.*t）;
plot（t,v2）;
legend（'curve'）
title（'Graphofv2=220.*exp（-5.*t）.*sin（2*pi*50.*t）'）
xlabel（'taxis'）
ylabel（'v-axis'）
gridon
3.Usesubplot,drawa2by2arrayofplotsforthefollowingfunctions:
ANSWER:
Applyappropriatelinetype,title,labelsandaxisrangesforthegraphs.
v_1=cos（10*pi*t）;
subplot（2,2,1）;
plot（t,v_1）;
xlabel（'t'）,ylabel（'v1'）
title（'Graphofv_1=cos（10*pi*t）'）
v_2=cos（10*pi*t）.*exp（-5*t）;
subplot（2,2,2）;
plot（t,v_2）;
xlabel（'t'）,ylabel（'v2'）
title（'Graphofv_2=cos（10*pi*t）.*exp（-5*t）'）
v_3=cos（10*pi*t）.*exp（-10*t）;
subplot（2,2,3）;
plot（t,v_3）;
xlabel（'t'）,ylabel（'v3'）
title（'Graphofv_3=cos（10*pi*t）.*exp（-10*t）'）
v_4=cos（10*pi*t）.*exp（-20*t）;
subplot（2,2,4）;
plot（t,v_4）;
xlabel（'t'）,ylabel（'v4'）
title（'Graphofv_4=cos（10*pi*t）.*exp（-20*t）'）
4.Useplot3toplot2spiralcurveslikebelowwithappropriatelinewidthandcolour.
ANSWER:
t=0:
0.001:
10;
z=0.2*t;
x=sin（2*pi.*t）.*z.*z;
y=cos（2*pi.*t）.*z.*z;
plot3（x,y,z,'g','LineWidth',2）;
holdon;
axis（[-44-4402]）;
holdoff;
z1=z.^0.5
x1=sin（2*pi.*t）.*（z1）
y1=cos（2*pi.*t）.*（z1）
plot3（x1,y1,z1,'r','LineWidth',2）;
5.Displaythesurfaceusingmeshandcontourwithasuitableresolution:
ANSWER:
[x,y]=meshgrid（-2:
.1:
2,-2:
.2:
2）;
f=exp（-0.005.*（（x-50）.^2+（y-50）.^2））;
figure
（1）;
mesh（x,y,f）;xlabel（'x'）;ylabel（'y'）;grid;
figure
（2）;contour（x,y,f）;
xlabel（'x'）;ylabel（'y'）;grid;
6.Load2ofyourphotosintoMatlabWorkSpaceusingimread.a）Changebrightnesslocallyorglobally.b）Overlapthemtoproduceanewphoto.c）writeanewphotointoafileusingimwrite.（Note:
lowerversionofMatlabsuchas6.5isnotallowedtodosomedirectimageoperations.）
ANSWER:
A=imread（'11.jpg'）;
B=imread（'22.jpg'）;
[MNP]=size（A）;
imshow（A+100）;
figure
（1）;
C=A+B（1:
M,1:
N,1:
P）;
imshow（C）;
figure
（2）;
imwrite（C,'33.jpg'）;
7.
theequationcoefficients:
A=[1-143
-545-6
07-89
-13-26];（M=N）
a）FindthedeterminantofA,
b）FindtheinverseofAandcheckformatrixsingularity,
c）IfB=[5;1;-2;3],findtheunknownxintheequation.
ANSWER:
a）det（A）
ans=
-765.0000
b）inv（A）
ans=
0.3333-0.00000.3333-0.6667
0.20000.11760.2706-0.3882
0.20000.05880.0353-0.0941
0.0222-0.0392-0.06800.2183
cond（A）
ans=
16.4186
c）x=inv（A）*b
ans=
-1.0000
-0.5882
0.7059
0.8627
8.Forlinearsimultaneousequations,
M>N,theequationcoefficients:
A=[1-143
-545-6
07-89
-13-26
1-253
147-3];
a）FindthedeterminantofA’*A,
b）FindtheinverseofA’*Aandcheckformatrixsingularity,
c）IfB=[5;1;-2;3;4;0],findthesolutionoftheequation.
ANSWER:
a）det（A'*A）
ans=
2.1051e+07
b）inv（A'*A）
ans=
0.08840.0321-0.0013-0.0219
0.03210.02310.0002-0.0099
-0.00130.00020.00850.0053
-0.0219-0.00990.00530.0144
cond（A'*A）
ans=
32.5278
c）x=inv（A'*A）*A'*B
x=
-0.8903
-0.4898
0.5755
0.7083
9.Dataof10recordsareshownbelow
y=[3.54.33.75.46.67.38.78.89.49.010.012.011.39.913.3],
Usepolyfitwithdifferentorders（from1to3）ofpolynomialstofindacurveofbestfit.Checkthetotaldistancebetweenthefittedcurvezandrecordsdefinedby
.
ANSWER:
x=linspace（0,1,15）;
y=[3.54.33.75.46.67.38.78.89.49.010.012.011.39.913.3];
plot（x,y,'x'）;
holdon;
p=polyfit（x,y,1）;
z=polyval（p,x）;
s1=sqrt（sum（（z-y）.^2））;%totaldistance
plot（x,z,'b','LineWidth',3）;
holdon;
%一次拟合
p=polyfit（x,y,2）;
z=polyval（p,x）;
s2=sqrt（sum（（z-y）.^2））;%totaldistance
plot（x,z,'r','LineWidth',3）;
holdon;
%二次拟合
p=polyfit（x,y,3）;
z=polyval（p,x）;
s3=sqrt（sum（（z-y）.^2））;%totaldistance
plot（x,z,'g','LineWidth',3）;
%三次拟合
holdoff;
gridon;
s1=
3.2807
s2=
3.0399
s3=
3.0398
10.Createasetof20pointsfromacurvebyMatlabcode:
x=1:
20;y=2*exp（-0.3*（x-5）.^2）+0.7*exp（-0.2*（x-12）.^2）;
Theninterpolatethecurveto60pointsusing‘linear’and‘spline’options,respectively.Seethequalityofdifferenttypesofinterpolation.
ANSWER:
xi=1:
0.25:
20;
yi=interp1（x,y,xi,'linear'）;
plot（x,y,'r*'）;holdon;
plot（xi,yi,'o'）;
plot（xi,yi,':
'）;
holdoff;
yi=interp1（x,y,xi,'spline'）;
figure
（2）;
plot（x,y,'r*'）;holdon;
plot（xi,yi,'o'）;
plot（xi,yi,':
'）;
holdoff;
PartB
1.Usingtheplotandsubplotfunctionscreate4plotsona2by2arrayofsubplots,forthefunctionexp（-t）sin（5t）showingineachplotthefunctioninthecorrespondingintervalsofti.e.（-2,-1）,（-1,0）,（0,1）and（1,2）.
Answer:
t=-2:
.01:
2;
x=exp（-t）.*sin（5.*t）;
subplot（2,2,1）;
plot（t,x）;axis（[-2,-1-2020]）;
subplot（2,2,2）;
plot（t,x）;axis（[-1,0-2020]）;
subplot（2,2,3）;
plot（t,x）;axis（[0,1-2020]）;
subplot（2,2,4）;
plot（t,x）;axis（[1,2-2020]）;
2.Athreephaseinductionmotorcharacteristicisgivenintermsofmechanicalshaftoutputtorque
（NMNewton-meter）asafunctionofrotationalspeedω（rad/sradianpersecond）.Thisisapproximatedby3piece-wiselinearequationsasfollows:
Thismotorisdirectlycoupledtoaload
whichcanberepresentedas
Write2separateMatlabfunctionm-filesinwhich:
a）themotorcharacteristic,b）theloadcharacteristicaredefinedonlyasfunctionsofω.Namethemmotor.mandsysload.m,respectively.
Answer:
w=0:
0.01:
120*pi;
a）Tm=（w>=0&w<=90*pi）.*w*（90*pi）+4+（w<=110*pi&w>90*pi）.*（-10*w/（pi）+1200）+（w>110*pi&w<=120*pi）.*（-10*w/（pi）+1200）;
plot（w,Tm）;
b）Tl=-50*（w/（120*pi））.^3+100*（w/（120*pi））.^2+4*w./（120*pi）;
3.WriteaMatlabscripgt-mfilewhichcallsyourfunctionm-filesfromQuestion2.Andplotthemotorandloadcharactersticsonthesamefigure,givingsuitablelabellingandtitle.Namethisscriptm-filesystemplot.m
Answer:
w=0:
pi/20:
120*pi;
plot（w,Tm,'m','LineWidth',2）; hold on;
plot（w,Tl,'r','LineWidth',2）; hold off;
xlabel（'speed w（rad/s_）'）;
ylabel（'torque（NM Newton-meter）'）;
title（'the motor and load characterstics'）;
legend（'motor line','sysload line'）
4.Writeasriptm-filewhichfindsallthemathematicallpossiblepoints（valuesofω）where
5.
fortherange0≤ω≤120π（rad/s）withthecharacteristicgiveninQuestion2.Thesystemcouldtheoreticallyoperateataspeedωwhere
Mathematically,thisinvolvesfindingtherootsoftheequation
Giveanametothism-fileposspoints.m.Callposspoints.minsystemplot.mandshowallofthepointsonasystemplotusingthe‘o’symbol.
Answer:
function[Tm]=tm（w）
Tm=（w>=0&w<=90*pi）.*w*（90*pi）+4+（w<=110*pi&w>90*pi）.*（-10*w/（pi）+1200）+（w>110*pi&w<=120*pi）.*（-10*w/（pi）+1200）;
end;
Function[T1]=t1（w）
Tl=-50*（w/（120*pi））.^3+100*（w/（120*pi））.^2+4*w./（120*pi）;
end
（2）x
（1）=fzero（@tm,[60,90]）; x
（2）=fzero（@tm,[300,320]）; x（3）=fzero（@tm,[350,370]）;
（3）w=0:
pi/20:
120*pi; Tm=tm（w）;
plot（w,Tm,'m','LineWidth',2）; hold on;
Tl=t1（w）;
plot（w,Tl,'r','LineWidth',2）; hold on;
xlabel（'speed w（rad/s_）'）;
ylabel（'torque（NM Newton-meter）'）;
title（'the motor and load characterstics'）; legend（'motor line','sysload line'） posspoints;
Tl=-50*（x/（120*pi））.^3+100*（x/（120*pi））.^2+4*x/（120*pi） plot（x,Tl,'ko','LineWidth',2）; hold off; grid on;
PartC
IntroductiontoDSP
1.Basicdigitalsignals
Unitimpulsefunction
Exercise1-1:
DisplaytheunitimpulsefunctionwithMatlabcode.ThecodecanbeeithertypedunderMatlabpromptorwrittenintoascriptMatlabfile,thenrunthefile.
n=-10:
10;
fork=1:
21
x（k）=0;
end;
x（11）=1;
stem（n,x）;
axis（[-101002]）;
Problem1-1:
Forthesignal
writetheMatlabcodeandcopytheresultfigureintothefollowingboxes.
n=-10:
10;
fork=1:
21
x（k）=0;
end;
x（9）=2;
stem（n,x）;
axis（[-101002]）;
Unitstepfunction
Exercise1-2:
DisplaytheunitstepfunctionwithMatlabcode:
n=-10:
10;
fork=1:
10
x（k）=0;
end;
fork=11:
21
x（k）=1;
end;
stem（n,x）;
axis（[-101002]）;
Problem1-2:
Forthesignal
writetheMatlabcode,anddisplaythecorrespondingsignalintothefollowingboxes.
n=-10:
10;
fork=1:
12
x（k）=0;
end;
fork=13:
21
x（k）=-1;
end;
stem（n,x）;
axis（[-1010-21]）;
Sinewave
where-frequency（rad/second）,T-samplinginterval（seconds）
Exercise1-3:
LetT=0.02,=6.28.Usingthefollowingcode,plotonthescreenintheregion0n100.
n=0:
100;
T=0.02;
omega=6.28;
fork=1:
101
x（k）=sin（（k-1）*omega*T）;
end;
stem（n,x）;
Exercise1-3:
LetT=0.02,=6.28.Usingthefollowingcode,plotonthescreenintheregion0n100.
n=0:
100;
T=0.02;
omega=6.28;
fork=1:
101
x（k）=sin（（k-1）*omega*T）;
end;
stem（n,x）;
Problem1-3:
Modifytheabovecodetodisplaythesignal:
whereT=0.02,=6.28.Executethecodeandplotthesignalonthescreen.Copythecode,thendisplaythesignalintothefollowingboxes.
n=0:
100;
T=0.02;
omega=6.28;
fork=1:
101
x（k）=2*sin（（k-1）*omega*T+pi/2）;
end;
stem（n,x）;
Timeshift,impulseandstepresponses
Exercise1-4
Fortheunitimpulse,
andtheunitstep
writetwoMatlabfunctionsands
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