lyl Lab Report1报告.docx
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lyl Lab Report1报告.docx
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lylLabReport1报告
LaboratoryReportofDigitalSignalProcessing
LabIII.FilterDesignandRealizationinMATLAB
Name:
岳成
No.:
5100309669
Date:
2013/4/24
SHANGHAIJIAOTONGUNIVERSITY
DepartmentofInstrumentScience&Engineering
Content
1Introduction1
2Exercises1
Ex.1Designaband-passEllipticfilter1
Ex.2AddechoestoMartinLutherKing’sspeech1
Ex.3Designadigitalequalizer2
3ResultsandDiscussion3
Ex.1Designaband-passEllipticfilter3
Ex.2AddechoestoMartinLutherKing’sspeech7
Ex.3Designadigitalequalizer9
4Summary11
5Reference11
1Introduction
ThislabconcentratesmainlyonthedesignandrealizationoffiltersinMATLAB.Theinfiniteimpulseresponse(IIR)filtersandfiniteimpulseresponse(FIR)filtersarecomparedtoeachotherforunderstandingtheircharacteristics.Besides,I/Odifferenceequationmethodiscarriedouttoconductfiltering.ApieceofpublicspeechofMartinLutherKingischosenasanexampletoshowtheeffectofechoesinonespeech.Inthefinal,adigitalequalizerisdesignedtochangeamusictodifferentstyle.Thislabincludesthefollowingexercises.
2Exercises
Ex.1Designaband-passEllipticfilter
1.1Referto‘IIRBUT.m’inthecourse,developananalogandadigitalband-passEllipticfilterwiththeMatlabfunction‘ellip’,respectively.Setthepropertiesofthefilter:
theordern=6,andthepassbandfrom400Hzto600Hz.ShowthefrequencyresponsesofMagnitudeandPhase.Providethecodesintheappendix.
1.2RefertotheMatlabfunction‘filter’,developasub-function‘myfilter’withtheinput/outputinterfaceof‘y=myfilter(b,a,x)’byusingtheI/Odifferenceequationmethod.Providethecodesof‘myfilter’inthereport.
1.3Createasignalcomposedofthreesinusoidsignalswithfrequenciesof100Hz,500Hzand1000Hz.Use‘myfilter’withthefiltercoefficientsoftheband-passfilterdevelopedin1.1toeliminatecomponentsof100Hzand1000Hz.Comparethesignalsbeforeandafterfilteringinboththetimedomainandthefrequencydomain.Providethecodesintheappendix.
Ex.2AddechoestoMartinLutherKing’sspeech
Aspeechcanbeheardmoreloudlyandstronglyinanemptyroomwithechoesthaninanopenareawithoutanyecho.However,iftheechoistoo‘strong’,thevoicewillbe‘blunt’andunclear.
ThegenerationofechoesisillustratedinFig.1,wheretheoutputsignalsoundy(t)isfedbackafteradelayTandscaledwithα.AndFig.1isthecorrespondingdiscrete-timesystemoftheechogeneration,wherethenumberofdelaysamplesis
andfsisthesamplingfrequencyofthesound.Typically,
assuccessiveechoesareattenuatednormally.
Fig.1Generatetheechointhecontinuous-anddiscrete-timesystems.
2.1AccordingtoFig.8,developthedifferenceequationofthesystemandcomparetheimpulseresponsesandthemagnitudesandphasesofthesystemwiththeparametersof
(1)
andk=5,10,100,respectively;
(2)k=10,and
respectively.
2.2Develop‘MyEcho.m’,importtheaudio‘dream.wav’andfilterthesoundwithadelaytimeT=0.5secandascale
.Thenplaythefilteredsoundtochecktheechoeffects.Providethecodesintheappendix.
Ex.3Designadigitalequalizer
In soundrecordingandreproduction, an equalizeriscommonlyusedtoalterthe frequencyresponse ofanaudiosystemusingagroupof linearfilters.An equalizer canbecircuitsforanalogsoundordigitalfiltersfordigitalsound.AsshowninFig.2,adigitalequalizerisaseriesoffilterswithdifferentgains.
3
3.1Constructanequalizerin‘myEQ.m’withasetoffilters.DesignthefilterseitherbyFDAtoolorbyMatlabfunctions.AgroupofanyIIRfiltersandagroupofanyFIRfiltersaredesignedtomeettherequirementsoftheequalizer,respectively.CutofffrequencyofeachfilterisillustratedinCht.1.
Cht.1Cut-offfrequencyofa5-filterequalizer
LPF1
BPF1
BPF2
BPF3
HPF1
fL(Hz)
60
250
1000
2000
fH(Hz)
60
250
1000
2000
3.2TunethegainofeachfilterandenjoydifferentsoundeffectwithparametersshowninCht.2.Chooseonesetofparametersanduseffttogetthefrequencyspectrumofboththeoriginalaudioandthetunedsignal.Plottheirspectrumtoseethedifference.Providethecodesintheappendix.
Cht.2Gainoptionsfordifferentstyles
α1
(dB)
α2
(dB)
α3
(dB)
α4
(dB)
α5
(dB)
Natural
0
0
0
0
0
Classic
0
80
80
40
0
Pop
30
10
0
-20
-40
Bass
80
60
0
-60
-80
Rock
-20
0
20
40
-20
3ResultsandDiscussion
Ex.1Designaband-passEllipticfilter
1.1
Fig.3ComparisonofFRFbetweendigitalandanalogfilter
labIII1_1.m
clc,clear,closeall
n=6;%order
Rp=0.5;Rs=20;
fl=400;wl=2*pi*fl;%lowband
fh=600;wh=2*pi*fh;%highband
df=0.001;
f=0:
df:
1000;w=2*pi*f;
%AnalogButterworthfilter(fHs)
[bs,as]=ellip(n,Rp,Rs,[wlwh],'s');
Hs=freqs(bs,as,w);
%DigitalButterworthfilter(fzHz)
fs=1500;
wnl=fl/(fs/2);
wnh=fh/(fs/2);
[bz,az]=ellip(n,Rp,Rs,[wnlwnh]);
[Hz,fz]=freqz(bz,az,1000,fs);
%showresults
figure
plot(fz,20*log10(abs(Hz)),f,20*log10(abs(Hs)),'r:
','linewidth',2);
legend('Digital','Analog','Location','northeast');
set(gca,'xscale','log')
xlim([1,1000])
ylim([-160,10])
xlabel('Frequency(Hz)')
ylabel('magnitude(dB)')
1.2
InI/Odifferenceequation,wecanuseexpression
togety[n].Beforethat,weshouldfirstgetx[i]andy[1]~y[n-1].
MyFilter.m
functionY=myfilter(b,a,x)
%%input
ifnargin<1
disp('NoInput!
');
return
end
B=b;
A=a;
X=x;
n=length(X);
m=length(A);
%%I/Odifferenceequation
l=0;
Y=zeros(1,n);
forjj=1:
m-1
forkk=1:
jj
ifkk==jj
l=B(kk)*X(jj-kk+1);
else
l=B(kk)*X(jj-kk+1)-A(jj-kk+1)*Y(kk);
end
Y(jj)=Y(jj)+l;
end
end
forii=m:
n
forkk=1:
m
ifkk==m
l=B(kk)*X(ii-kk+1);
else
l=B(kk)*X(ii-kk+1)-A(m-kk+1)*Y(ii-m+kk);
end
Y(ii)=Y(ii)+l;
end
end
%%outputresults
y=Y;
end
1.3
Fromthefigure,wecanseetheband-passfiltercandobetterinsignalprocessing,butthesignalwegetintimedomaindoesn’tlookwell.That’sbecausewecan’tfilterthesignalcompletelysothere’salsoalittleinterferenceinthesignal.
Fig.4FilteringaSignalswithEllipticFilter
abIII1_3.m
clc,clear,closeall
ord=6;%order
fs=10000;
Rp=0.5;Rs=20;
fl=400;wl=fl/(fs/2);%lowband
fh=600;wh=fh/(fs/2);%highband
[b,a]=ellip(ord,Rp,Rs,[wlwh]);
[Hz,fz]=freqz(b,a,1000,fs);
%%creatanimpulsesignal
fs_imp=100;
T_imp=1;
t_imp=0:
1/fs_imp:
T_imp;
imp=[1;zeros(length(t_imp)-1,1)];
%filterimpulsesignal
h_imp=MyFilter(b,a,imp);
%%createsignalswiththreedifferentfrequencies
f1=100;f2=500;f3=1000;
t=-1/f1:
1/fs:
1/f1;
n=length(t);
x1=sin(2*pi*f1*t);
x2=sin(2*pi*f2*t);
x3=sin(2*pi*f3*t);
x=x1+x2+x3;
%plot(t,x);
X=abs(fft(x)/(n/2));
F_X=fs*(0:
1/n:
1-1/n);
%%filterthesignal
h=MyFilter(b,a,x);
H=abs(fft(h)/(n/2));
F_H=fs*(0:
1/n:
1-1/n);
%%showresults
figure
subplot(3,2,1);plot(t,x,'linewidth',2);%xintimedomain
title('x(t)');
subplot(3,2,2);plot(F_X,X,'linewidth',2);%xinfrequencydomain
xlim([0,2000]);
title('X(j\omega)')
subplot(3,2,3);plot(t_imp,h_imp,'linewidth',2);%hintimedomain
title('h(n)')
subplot(3,2,4);plot(fz,abs(Hz),'linewidth',2);%hinfrequencydomain
xlim([0,1000]);
title('H(\omega)')
subplot(3,2,5);plot(t,h,'linewidth',2);%yintimedomain
title('y(t)')
xlabel('Time(s)')
subplot(3,2,6);plot(F_H,H,'linewidth',2);%yinfrequencydomain
xlim([0,2000]);
title('Y(j\omega)')
xlabel('Frequency(Hz)')
%%end
Ex.2AddechoestoMartinLutherKing’sspeech
2.1
Thefollowingsixfiguresshowstheresultsintheimpulseresponses,themagnitudesandphasesofthesystemwithdifferentparametersofkanda.Wewilltalkaboutthemrespectively.
Fig.5ImpulseResponsewithDifferentk
Thethreefiguresshowstheresultswithdifferentdelayk,inwhichFig.5showstheimpulseresponses,Fig.6showsthemagnitudesandFig.7showsthephases.
Fig.6MagnitudeswithDifferentk
Fig.7PhaseswithDifferentk
Thesethreefiguresshowstheresultswithdifferentscalea,inwhichFig.8showstheimpulseresponses,Fig.9showsthemagnitudesandFig.10showsthephases.Fromthesefigureswecanseethatdifferentaonlyaffecttheamplitudeinbothmagnitudesandphases,butthefrequencyisthesame.
Fig.8ImpulseResponsewithDifferenta
Fig.9MagnitudeswithDifferenta
Fig.10PhaseswithDifferenta
2.2
MyEcho.m
clc,clear,closeall
%getthewavefromdream.wav
[x_dream,fs,NBITS]=wavread('dream.wav');
x_cut=x_dream(1:
5*fs,1);
sound(x_cut);
%setparameters
T=0.5;
k=T*fs;
a=0.2;
%getthewavewithechoes
y=zeros(1,length(x_cut));
forii=1:
k
y(ii)=x_cut(ii);
end
forii=k+1:
length(x_cut)
y(ii)=a*y(ii-k)+x_cut(ii);
end
sound(y);
Ex.3Designadigitalequalizer
3.2
Fig.11DifferentFilterandSignalsthroughEachFilter
Fig.12OriginalAudio(up)andTunedClassicSignal(down)
Fig.11showsthefiltersandsignalsthrougheachfilter,Fig.12showstheoriginalaudio(up)andthetunedClassicsignal(down).
myEQ.m
clc,clear,closeall
%%
[x,fs,NBITS]=wavread('canon.wav');
x_cut=x(1:
10*fs,1);
%sound(x_cut);
%%somedefinition
Natural=[00000];
Classic=[08080400];
Pop=[30100-20-40];
Bass=[80600-60-80];
Rock=[-2002040-20];
style=cell(1,5);
style{1}=Natural;style{2}=Classic;
style{3}=Pop;style{4}=Bass;
style{5}=Rock;
filt=cell(1,5);
filt{1}='IIR_LPF.mat';filt{2}='IIR_BPF1.mat';
filt{3}='IIR_BPF2.mat';f
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