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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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