东南大学短学期MATLAB作业MatlabWorksheet2.docx
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东南大学短学期MATLAB作业MatlabWorksheet2
MatlabWorksheet2
PartA（In-classroomexercises）
1.Usingplottodisplaythefollowingvoltagewithappropriatelinetype,titleandlabels.Alsopresentthegraphwithsuitablerangesofaxis.
wheref=50Hz.
（Hint:
timeintervalmustbesmallenough,e.g.0.001seconds.Therefore,t=0:
0.001:
1isappropriate）;
closeall
f=50;
t=0:
1/3000:
1;
v=220*sin（2*pi*f*t）;
plot（t,v）;
xlabel（'t'）;
ylabel（'v'）;
title（'v（t）=220sin2\pift'）;
axis（[00.03-max（v）*1.5max（v）*1.5]）;
2.Usingplottodisplaythefollowingvoltagewithappropriatelinetype,titleandlabels.Alsopresentthegraphwithsuitablerangesofaxis.
wheref=50Hz.
Inaddition,onthesamegraph,drawtheenvelopeoftheoscillationandaddlegends.
closeall
f=50;
t=0:
1/1000:
1;
v=220*exp（-5*t）.*sin（2*pi*f*t）;
plot（t,v）;
xlabel（'t'）;
ylabel（'v'）;
title（'v（t）=220sin2\pift'）;
holdon;
v2=220*exp（-5*t）;
plot（t,v2,'r'）;
plot（t,-v2,'r'）;
legend（'theoscillation','theenvelopeoftheoscillation'）;
axis（[00.5-max（v）*1.5max（v）*1.5]）;
3.Usesubplot,drawa2by2arrayofplotsforthefollowingfunctions:
Applyappropriatelinetype,title,labelsandaxisrangesforthegraphs.
closeall
t=0:
0.01:
1;
v1=cos（10*pi*t）;
v2=exp（-5*t）.*cos（10*pi*t）;
v3=exp（-10*t）.*cos（10*pi*t）;
v4=exp（-20*t）.*cos（10*pi*t）;
subplot（221）;
plot（t,v1）;xlabel（'t'）;ylabel（'v1'）;title（'v（t）=cos（10\pit）'）;
holdon;
subplot（222）;
plot（t,v2）;xlabel（'t'）;ylabel（'v2'）;title（'v（t）=e^{-5}cos（10\pit）'）;
subplot（223）;
plot（t,v3）;xlabel（'t'）;ylabel（'v3'）;title（'v（t）=e^{-10}cos（10\pit）'）;
subplot（224）;
plot（t,v4）;xlabel（'t'）;ylabel（'v4'）;title（'v（t）=e^{-20}cos（10\pit）'）;
4.Useplot3toplot2spiralcurveslikebelowwithappropriatelinewidthandcolour.
closeall
t=0:
0.01*pi:
20*pi;
x=t.^2.*sin（t）;
y=t.^2.*cos（t）;
z=5*t;
subplot（121）;
plot3（x,y,z,'g'）;
holdon;
x=t.^0.5.*sin（t）;
y=t.^0.5.*cos（t）;
subplot（122）;
plot3（x,y,z,'r'）;
5.Displaythesurfaceusingmeshandcontourwithasuitableresolution:
closeall
[x,y]=meshgrid（0:
1:
100,0:
1:
100）;
z=exp（-0.005*（（x-50）.^2+（y-50）.^2））;
figure
（1）;mesh（x,y,z）;
figure
（2）;contour（x,y,z）;
6.Load2ofyourphotosintoMatlabWorkSpaceusingimread.a）Changebrightnesslocallyorglobally.b）Overlapthemtoproduceanewphoto.c）writeanewphotointoafileusingimwrite.（Note:
lowerversionofMatlabsuchas6.5isnotallowedtodosomedirectimageoperations.）
closeall
small=imread（'small.png'）;
big=imread（'big.png'）;
b_size=size（big）;
s_size=size（small）;
small（b_size
（1）,b_size
（2）,b_size（3））=0;
form=1:
s_size
（1）
forn=1:
s_size
（2）
forp=1:
s_size（3）
big（m,n,p）=small（m,n,p）;
end
end
end
imshow（big）;
imwrite（big,'new.png'）;
7.Forlinearsimultaneousequations
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
Aisnotsingular.
c）>>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=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:
m-file:
closeall
x=1:
1:
15;
y=[3.54.33.75.46.67.38.78.89.49.010.012.011.39.913.3];
p1=polyfit（x,y,1）;z1=polyval（p1,x）;
p2=polyfit（x,y,2）;z2=polyval（p2,x）;
p3=polyfit（x,y,3）;z3=polyval（p3,x）;
plot（x,y,'ro'）;holdon;
plot（x,z1,'b','LineWidth',2）;
plot（x,z2,'m','LineWidth',2）;
plot（x,z3,'k','LineWidth',2）;
legend（'point','polyfit1','polyfit2','polyfit3',2）;
s1=sqrt（sum（（z1-y）.^2））
s2=sqrt（sum（（z2-y）.^2））
s3=sqrt（sum（（z3-y）.^2））
CommandWindow:
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:
closeall
x=1:
20;y=2*exp（-0.3*（x-5）.^2）+0.7*exp（-0.2*（x-12）.^2）;
xi=1:
1/3:
20;
y1=interp1（x,y,xi,'linear'）;
y2=interp1（x,y,xi,'spline'）;
plot（x,y,'k.'）;holdon;
plot（xi,y1,'r'）;
plot（xi,y2,'b'）;
legend（'initial','linear','spline',1）;
PartB
1.Usingtheplotandsubplotfunctionscreate4plotsona2by2arrayofsubplots,forthefunctionexp（-t）sin（5t）showingineachplotthefunctioninthecorrespondingintervalsofti.e.（-2,-1）,（-1,0）,（0,1）and（1,2）.
Answer:
closeall;clearall;
t=-2:
0.01:
-1;
y=exp（-t）.*sin（5*t）;
subplot（221）;plot（t,y）;
t=-1:
0.01:
0;
subplot（222）;plot（t,y）;
t=0:
0.01:
1;
subplot（223）;plot（t,y）;
t=1:
0.01:
2;
subplot（224）;plot（t,y）;
2.Athreephaseinductionmotorcharacteristicisgivenintermsofmechanicalshaftoutputtorque
（NMNewton-meter）asafunctionofrotationalspeedω（rad/sradianpersecond）.Thisisapproximatedby3piece-wiselinearequationsasfollows:
Thismotorisdirectlycoupledtoaload
whichcanberepresentedas
Write2separateMatlabfunctionm-filesinwhich:
a）themotorcharacteristic,b）theloadcharacteristicaredefinedonlyasfunctionsofω.Namethemmotor.mandsysload.m,respectively.
Answer:
function[Tm]=motor（w）
forn=1:
length（w）
ifw（n）>=0&&w（n）<=90*pi
Tm（n）=w（n）/（90*pi）+4.0;
elseifw（n）<110*pi
Tm（n）=95*w（n）/（20*pi）-422.5;
elseifw（n）<=120*pi
Tm（n）=-10*w（n）/pi+1200;
end
end
sysload.m:
function[Tl]=sysload（w）
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:
systemplot.m:
closeall;
w=0:
pi/3:
120*pi;
plot（w,motor（w）,'r'）;holdon;
plot（w,sysload（w）,'k'）;
legend（'motor','sysload',2）;
4.Writeasriptm-filewhichfindsallthemathematicallpossiblepoints（valuesofω）where
5.
fortherange0≤ω≤120π（rad/s）withthecharacteristicgiveninQuestion2.Thesystemcouldtheoreticallyoperateataspeedωwhere
Mathematically,thisinvolvesfindingtherootsoftheequation
Giveanametothism-fileposspoints.m.Callposspoints.minsystemplot.mandshowallofthepointsonasystemplotusingthe‘o’symbol.
Answer:
posspoints.m:
t=0:
0.01:
120*pi;
sub=motor（t）-sysload（t）;
ansLoc=1;
forn=2:
length（sub）
p=sub（n）;
q=sub（n-1）;
ifp*q<0
xSet（ansLoc）=t（n）;
ansLoc=ansLoc+1;
end
end
systemplot;holdon;
plot（xSet,motor（xSet）,'o'）;
xSet
CommandWindow:
>>posspoint
xSet=
74.0200307.6800360.7900
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）;
Problem1-3:
Modifytheabovecodetodisplaythesignal:
whereT=0.02,=6.28.Executethecodeandplotthesignalonthescreen.Copythecode,thendisplaythesignalintothefollowingboxes.
n=0:
100;
T=0.02;
omega=6.28;
x=2*sin（n*omega*T+pi/2）;
stem（n,x）;
Timeshift,impulseandstepresponses
Exercise1-4
Fortheunitimpulse,
andtheunitstep
writetwoMatlabfunctionsandsaveas‘impseq.m’and‘stepseq.m’files,respectively.
%impseq.m
%UnitImpulse
%[n1:
n2]simplenumberrange
%n0-timeshift
function[x,n]=impseq（n0,n1,n2）
n=[n1:
n2];
x=[（n-n0）==0];
%end;
%stepseq.m
%UnitStep
%[n1:
n2]simplenumberrange
%n0-timeshift
function[x,n]=stepseq（n0,n1,n2）
n=[n1:
n2];
x=[（n-n0）>=0];
%end
Giventhefollowingdifferenceequation:
a）Calculateandplottheimpulseresponseatn=-20,…,120;and
b）Calculateandplotthestepresponseatn=-20,…,120,usingthefollowingcode
b=[1];a=[1,-0.7,0.9];
x=impseq（0,-20,120）;
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