数字滤波器设计英文文献.doc
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数字滤波器设计英文文献.doc
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DigitalFilterDesignUsingMatlab
ByTimothyJ.Schlichter
EE4000IntroductiontoDigitalFiltering
5/2/99
Submittedto:
Dr.JosephPicone
MississippiStateUniversity
DepartmentofElectricalandComputerEngineering
EXECUTIVESUMMARY
Afundamentalaspectofsignalprocessingisfiltering.Filteringinvolvesthemanipulation
ofthespectrumofasignalbypassingorblockingcertainportionsofthespectrum,
dependingonthefrequencyofthoseportions.Filtersaredesignedaccordingtowhatkind
ofmanipulationofthesignalisrequiredforaparticularapplication.Digitalfiltersare
implementedusingthreefundamentalbuildingblocks:
anadder,amultiplier,andadelay
element.
Thedesignprocessofadigitalfilterislongandtediousifdonebyhand.Withtheaidof
computerprogramsperformingfilterdesignalgorithms,designingandoptimizingfilters
canbedonerelativelyquickly.ThispaperdiscussestheuseofMatlab,amathematical
softwarepackage,todesign,manipulate,andanalyzedigitalfilters.
ThedesignoptionsinMatlaballowtheusertoeithercreateacodefordesigningfilters
thatcallsbuilt-infunctions,ortodesignfiltersinSptool,agraphicaluserinterface.Each
ofthesemethodsareexaminedinthispaper.Thestrengthsandweaknessesofeachare
detailedinthefollowingdiscussion.
ThispaperconcludeswithadiscussionofhowthedatagivenbyMatlabforvariousfilters
canbeusedtoimplementfiltersonrealdigitalsignalprocessors.Matlabprovidesallthe
informationnecessaryforbuildingahardwarereplicaofthefilterdesignedinsoftware.
TABLEOFCONTENTS
1.Abstract……………………………………………………………..4
2.Introduction.………………………………………………………..4
3.LowpassFilterDesign………………………………………………7
4.HighpassandBandpassFilterDesign………………………………11
5.Sptool……………………………………………………………….13
6.FutureDirections……………………………………………………16
7.Acknowledgments…………………………………………………..16
8.References…………………………………………………………..16
9.Appendix…………………………………………………………….17
Abstract
Matlabprovidesdifferentoptionsfordigitalfilterdesign,whichincludefunctioncallsto
filteralgorithmsandagraphicaluserinterfacecalledSptool.Avarietyoffilterdesign
algorithmsareavailableinMatlabforbothIIRandFIRfilters.Thispaperdiscussesthe
differentoptionsinMatlabandgivesexamplesoflowpass,highpass,andbandpassfilter
designs.
ResultsshowthatthegraphicaluserinterfaceSptoolisaquickerandsimpleroptionthan
theoptionofmakingfunctioncallstothefilteralgorithms.Sptoolhasamoreuser-
friendlyenvironmentsincethespectrumofthefilterisimmediatelydisplayedtotheuser,
andtheusercanquicklyzoominandexamineparticularareasofinterestinthespectrum
(i.e.thepassband).However,theshortcomingofSptoolisthatitonlydisplaysthe
magnituderesponseofthefilter,notthephaseresponse.
Introduction
Akeyelementinprocessingdigitalsignalsisthefilter.Filtersperformdirect
manipulationsonthespectraofsignals.Tocompletelydescribedigitalfilters,threebasic
elements(orbuildingblocks)areneeded:
anadder,amultiplier,andadelayelement.The
adderhastwoinputsandoneoutput,anditsimplyaddsthetwoinputstogether.The
multiplierisagainelement,anditmultipliestheinputsignalbyaconstant.Thedelay
elementdelaystheincomingsignalbyonesample.Digitalfilterscanbeimplemented
usingeitherablockdiagramorasignalflowgraph.Figure1showsthethreebasic
elementsinblockdiagramform,andFigure2showstheminsignalflowgraphform.
Withthebasicbuildingblocksathand,thetwodifferentfilterstructurescaneasilybe
implemented.ThesetwostructuresareInfiniteImpulseResponse(IIR)andFinite
ImpulseResponse(FIR),dependingontheformofthesystem’sresponsetoaunitpulse
input.IIRfiltersarecommonlyimplementedusingafeedback(recursive)structure,while
FIRfiltersusuallyrequirenofeedback(non-recursive).
InthedesignofIIRfilters,acommonlyusedapproachiscalledthebilinear
transformation.Thisdesignbeginswiththetransferfunctionofananalogfilter,then
performsamappingfromthes-domaintothez-domain.Usingdifferentialequations,it
canbeshown(Proakis677)thatthemappingfromthes-planetothez-planeis
ThismappingresultsinageneralformforanIIRfilterwithanarbitrarynumberofpoles
andzeros.Thesystemresponseandthedifferenceequationforthisfilterisasfollows:
Thissystemresponsecanbeeasilyrealizedusingasignalflowgraph
AnFIRfilterhasadifferenceequationof
Bytakingthez-transform,thesystemresponseis
TherealizationofanFIRfilterusingasignalflowgraphisstraightforward.
MatlabhasseveraldesignalgorithmsthatcanbeusedtocreateandanalyzebothIIRand
FIRdigitalfilters.TheII
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