基于matlab的fir数字滤波器设计与仿真（design and simulation of fir digital filter based on matlab）

基于MATLAB的FIR数字滤波器设计与仿真（DESIGNANDSIMULATIONOFFIRDIGITALFILTERBASEDONMATLAB）PROGRAMMABLEDEVICEAPPLICATIONSELECTRONIC,MEA,SUREMENT,T,ECHNOLOGYTHIRTYTHIRDVOLUME,ELEVENTHISSUENOVEMBER2010DESIGNANDSIMULATIONOFFIRDIGITALFILTERBASEDONMATLABWANGXUEFEIDEPARTMENTOFRADARENGINEERING,PLA,ORDNANCEENGINEERINGCOLLEGE,SHIJIAZHUANG050003DIGITALFILTERDESIGNANDAPPLICATIONOFDIGITALSIGNALPROCESSINGISONEOFTHECORECONTENTUSINGTHEMATLABSIGNALPROCESSINGTOOLBOXTHEFDATOOLTOOLDESIGNEDAFINITEIMPULSERESPONSEFILTERWITHDENOISINGFILTERINGFUNCTION,ANDACCORDINGTOTHEDIFFERENTAPPLICATIONREQUIREMENTSOFTHEFILTER,THEFDATOOLTOOLISUSEDTODESIGNTHEFILTERTHEFINITEIMPULSERESPONSEFILTERWITHDIFFERENTFILTERINGFUNCTIONSISDESIGNED,ANDTHEPARAMETERSCANBEADJUSTEDATANYTIMEACCORDINGTOTHEDESIGNREQUIREMENTSANDFILTERCHARACTERISTICSITISINTUITIVE,SIMPLEANDGREATLYALLEVIATEDTHEWORKLOADGREATLYFACILITATESTHEDESIGNOFTHEFILTERANDACHIEVESTHEIDEALAPPLICATIONPURPOSEFINALLY,THEDESIGNEDFILTERISSIMULATEDANDVERIFIEDTOCONTAINNOISETHENOISEOFTHESIGNALISANALYZEDBYCOMPARINGANDANALYZINGTHESIGNALINTIMEDOMAINANDFREQUENCYDOMAINBEFOREANDAFTERTHEFILTERDENOISINGTHEOBTAINEDFILTERCANACHIEVETHEDESIREDPERFORMANCENOISEEFFECTKEYWORDSDIGITALFILTERFINITEIMPULSEFILTERFDATOOLSIMULATIONCLCNUMBERTN713DOCUMENTIDENTIFICATIONCODEAMATLABBASED,FIR,F,IGURE,WAVE,FILTER,DESIGN,AND,EMULATIONMAYUEHONGMAYANHENGWANGXUEFEIDEPARTMEN,T,OF,OPT,ORADAR,ENDINEERING,ORDNANCE,ENGINEERING,COLL,EGE,SH,IJIAZ,HUANG,ABSTRACT,DIG,ITAL,FILTER,AND,APPLICATIO,N,OF,DIGIT,AL,SIGNAL,PR,OCESSING,IS,ONE,O,F,THE,COR,E,IN,THIS,PAPER,DESIGN,MATLABSIGNAL,PRO,CESSING,TOO,LBOX,OL,TO,OLS,DESIGNED,W,ITH,THE,DENO,ISING,FILTERING,F,FDATO,INITE,IMPULSE,RESPONSE,FILTER,ACCO,RDINGT,O,THE,DIFFERENT,APPLICAT,IONS,ISSUED,BY,FDATO,OL,TO,OL,DESIG,N,FEATURES,OF,DIFFERENT,FILT,FILTER,ER,RESPONSE,FINITE,IMPULSEF,ILTER,AND,BASED,ON,ILTER,CHAR,ACTER,ISTICS,OF,THE,DESIGN,REQUIREMENTS,AND,ADJUST,THE,PAR,AMET,ERS,AT,ANY,TIME,INTUITIVE,F,ANDEASY,G,REATLY,REDUCING,WO,RKLOAD,GR,EAT,LY,FACILITATE,THE,N,OF,THE,FILT,ER,TO,DESIG,ACHIEVE,THE,DESIR,ED,THE,APPLICATIO,NPURPOSE,FINALLY,THE,DESIGNED,FILTER,T,FILTER,SIMULATION,THE,SIGNAL,W,ITH,NOISE,DENO,ISING,DENOISING,F,O,ILTER,THROUG,H,ACOMPAR,ATIVE,ANALYSIS,BEFO,AND,AFT,ER,THE,SIG,IN,T,IME,DOMAIN,AND,F,REQUENCY,DOMAIN,W,AVEFORMS,O,NAL,BTA,INED,RE,BY,THEDESIG,NED,FILTER,CAN,ACHIEV,E,T,HE,DESIRED,DENOISING,EFFECTKEYWORDS,DIGITAL,FILTERFIRFDATOOLSIMULINK0LEADWITHTHEDEVELOPMENTOFINFORMATIONANDDIGITALTECHNOLOGY,DIGITALSIGNALPROCESSING12HASBECOMEONEOFTHEMOSTIMPORTANTSUBJECTSANDTECHNICALFIELDSTODAYITISINCOMMUNICATION,VOICE,IMAGES,AUTOMATICCONTROL,RADAR,MILITARY,AEROSPACE,MEDICALANDHOUSEHOLDAPPLIANCES,ETCMANYFIELDSHAVEBEENWIDELYUSEDBASICASPECTSOFDIGITALSIGNALPROCESSINGITUSUALLYINVOLVESTRANSFORMATION,FILTERING,SPECTRUMANALYSIS,MODULATION,DEMODULATIONANDCODINGCODEANALYSISANDPROCESSINGAMONGTHEM,FILTERINGISONEOFTHEMOSTWIDELYUSEDLINKS,THETHEORYOFDIGITALFILTER,34ANDRELATEDDESIGNHAVEALSOBEENSTUDIEDONEOFTHEPRIORITIES1PRINCIPLEANDDESIGNOFFIRFILTER11DESIGNPRINCIPLETHEUNITSAMPLINGRESPONSEOFTHEFIRFILTERISALWAYSFINITE,ANDITSSYSTEMFUNCTIONSNUMBERMAYBERECORDEDASHZMN0BNZN1THECOEFFICIENTSB0,B1,ANDBMARETHEUNITSAMPLINGRESPONSESOFTHESYSTEM,H0,H1,HM,ANDWHENNM,HN0SEENFROMTHETOPUPTHEFIRSYSTEMHASONLYZEROS,SOTHEFILTERSARENOTLIKETHEIIRFILTERITISEASYTOOBTAINBETTERPASSBANDANDSTOPBANDATTENUATIONCHARACTERISTICSTOMAKEAGOODDECLINEREDUCTIONCHARACTERISTICSGENERALLYREQUIRETHATTHEORDEROFHZBEOFSECONDARYHEIGHT,IE,MISLARGEFIRFILTER56HASITSOWNOUTSTANDINGADVANTAGESONEISTHATTHESYSTEMISALWAYSSTABLE,ANDTHEOTHERISITISEASYTOIMPLEMENTLINEARPHASE,ANDTHETHIRDISTOALLOWDESIGNOFMULTIPASSBANDORMULTIBANDFILTERWAVEORGANINMANYCASES,THEDESIGNEDFILTERHASLINEARPHASECHARACTERISTICSOFTHETRANSMISSIONFUNCTIONOFTHEFILTERISHEJHEJ2MODEHISAMPLITUDEFREQUENCYCHARACTERISTIC,ANDWISPHASEFREQUENCYCHARACTERISTICLINEARPHASECHARACTERISTICREFERSTOTHEFILTERPHASESHIFTANDFREQUENCYLINEARRELATIONSHIP,THATIS366MAYUEHONG,ETCMATLABBASEDFIRDIGITALFILTERDESIGNANDSIMULATIONOFTHEELEVENTHPHASEFORMULACONSTANTIF0,0ISCONSTANT,ALSOKNOWNASTHEPHASEFREQUENCYLINEARPHASESINCETHEFIRSYSTEMISANALLZEROSYSTEM,ITSUNITSAMPLINGTHERESPONSEISFINITE,SOITISEASYTOIMPLEMENTSOMESYMMETRYANDOBTAINLINEARITYPHASEWHENTHEUNITSAMPLINGRESPONSEOFTHEFIRFILTERISFINITE,ITISSATISFIEDHNHN1N,FIRFILTERISSTRICTLYLINEARPHASECHARACTERISTICTHEFIRFILTERDOESNOTHAVETHEOUTPUTFEEDBACKTOTHEINPUTINTHESTRUCTURETHEREISNOLOOPINTHEFLOWGRAPHFIG1SCHEMATICDIAGRAMOFMORDERFIRFILTEROPERATION1SHOWSFIGURE1FIRFILTERSTRUCTURETHECOREIDEAOFTHEDESIGNOFFIRDIGITALFILTERSISTOOBTAINFINITEPULSESTHERESPONSEAPPROXIMATESTHEGIVENFREQUENCYRESPONSETHECURRENTDESIGNMETHODSAREMAINLYUSEDTHEREAREWINDOWFUNCTIONMETHOD,FREQUENCYSAMPLINGMETHODANDEQUALRIPPLEAPPROXIMATIONMETHODINTHISPAPER,AWINDOWLETTERISAPPLIEDDESIGNOFFIRDIGITALFILTERBYNUMBERMETHODTHEKERNELOFTHEWINDOWFUNCTIONMETHODISGIVENFROMTHEGIVENTHEFREQUENCYCHARACTERISTICISDETERMINEDBYADDINGAWINDOWTOTHEFINITELONGUNITIMPULSERESPONSESEQUENCEHNWINDOWINGISDONEBYMAKINGTHEINFINITELONGPULSEOFANIDEALFILTERRESPONDTOHDNMULTIPLYTHEWINDOWFUNCTIONWNTOPRODUCEATRUNCATEDIMPULSERESPONSEHNHDNWN4RELATIVELYCOMMONWINDOWFUNCTIONINENGINEERING,61RECTANGULARWINDOWRECTANGULARWINDOWSARETHEMOSTWIDELYUSEDTHEADVANTAGEOFTHISWINDOWISTHEMAINVALVERATIOMORECONCENTRATED,THEDRAWBACKISTHATTHEREISANOBVIOUSGIBBSEFFECT,WITHHIGHERSIDELOBELEVELSANDSIDEEFFECTSTHEVALVECAUSESHIGHFREQUENCYINTERFERENCEANDLEAKAGEINTHETRANSFORM,ANDEVENNEGATIVESPECTRUMOCCURSPHENOMENON2TRIANGULARWINDOWTHETRIANGULARWINDOWISWIDERTHANTHERECTANGULARWINDOW,ANDTHEWIDTHOFTHEMAINLOBEISAPPROXIMATELYEQUALTOTHERECTANGLETWOTIMESTHEWINDOW,BUTTHESIDELOBEISSMALL,ANDTHEREISNOSIDELOBE3HANNINGWINDOWHANNINGWINDOWCALLEDTHERAISEDCOSINEWINDOW,HANNINGWINDOWCANBESEENASTHESUMOFTHESPECTRUMOF3RECTANGULARWINDOWS,WHICHCANCANCELEACHOTHERBYUSINGSIDELOBECANCELLATIONFREQUENCYINTERFERENCEANDLEAKAGEENERGYCOMPAREDWITHTHERECTANGULARWINDOW,HANNINGWINDOWMAINLOBEWIDENINGFREQUENCYTHEDISCRIMINATIONRATEDECREASESWHILETHESIDELOBEDECREASESSIGNIFICANTLYANDTHEATTENUATIONRATEISFASTER4HAMMINGWINDOWHAMMINGWINDOWISALSORAISEDCOSINEWINDOW,ALSOKNOWNASIMPROVEDTHERAISEDCOSINEWINDOW,HANNINGWINDOWISCOMPAREDWITHTHEDIFFERENTWEIGHTEDCOEFFICIENTS,THEWIDTHOFTHEMAINLOBEOFALIKE,BUTTHESIDELOBEATTENUATIONSPEEDISSLOWERTHANCHINESENINGWINDOWTHEREAREALSOBLACKMANBLACKMANWINDOWSANDSOONTHESELECTIONPRINCIPLEOFWINDOWFUNCTIONIS1HASALOWERSIDELOBEAMPLITUDE,ESPECIALLYTHEFIRSTSIDELOBEAMPLITUDE2THESIDELOBEAMPLITUDEDECREASESANDTHEVELOCITYISLARGE,SOTHATTHESTOPBANDATTENUATIONCANBEINCREASED3THEWIDTHOFTHEMAINLOBESHOULDBENARROWTOOBTAINASTEEPERTRANSITIONZONETHECOMPARISONOFTHEPARAMETERSOFTHESEWINDOWFUNCTIONSISSHOWNINTABLE1TABLE1COMPARISONOFSEVERALCOMMONWINDOWFUNCTIONPARAMETERSWINDOWFUNCTIONSIDELOBEPEAKATTENUATION/DBMAINLOBEWIDTH/MMINIMUMSTOPBANDATTENUATION/DBRECTANGULARWINDOW13421TRIANGULARWINDOW25825HANNINGWINDOW31844HAMMINGWINDOW41853BLACKMANWINDOW571274INGENERAL,THESECONDITIONSOFWINDOWFUNCTIONSAREDIFFICULTTOSATISFYATTHESAMETIME,WHENTHEMAINVALVEWIDTHISCHOSENALTHOUGHTHEBANDISNARROWER,THETRANSITIONBANDANDSTOPBANDFLUCTUATIONAREOBTAINEDALTHOUGHTHETRANSITIONBANDISSTEEPEROBVIOUSLYINCREASE,WHENCANCHOOSETHESMALLESTSIDELOBEAMPLITUDE,ALTHOUGHCANOBTAINTHEUNIFORMSLIPAMPLITUDEDEGREERESPONSEANDSMALLERSTOPBANDFLUCTUATION,BUTTHETRANSITIONBANDWIDENSTHEREFORE,THEACTUALELECTIONTHEWINDOWFUNCTIONSUSEDAREOFTENTHEIRTRADEOFFTHEWIDTHOFTHEMAINVALVEISGUARANTEEDTOBEONEUNDERSPECIFIEDCONDITIONS,THEMAINLOBEWIDTHISPROPERLYSACRIFICEDINRETURNFORSIDELOBEFLUCTUATIONSDECREASETHISPAPERUSESTHESPECIALIZEDTOOLSOFFILTERDESIGNPROVIDEDBYMATLABBOXFDATOOL68FILTERDESIGNANALYSISTOO1SIMULATIONDESIGNFILTERS,YOUCANCHOOSEDIFFERENTWINDOWFUNCTIONSACCORDINGTODIFFERENTTECHNOLOGIESASWELLASTHEORDEROFTHEFILTER,THEFIRNUMBERISDESIGNEDTOSATISFYTHEAMPLITUDEANDPHASEREQUIREMENTSWORDFILTER12DESIGNREQUIREMENTSFDATOOLISTHEFILTERUSEDINTHEMATLABSIGNALPROCESSINGTOOLBOXWAVEDESIGNANDANALYSISTOOLFDATOOLCANDESIGNALMOSTALLOFTHEBASICCONVENTIONALFILTERSINCLUDEVARIOUSDESIGNMETHODSFORFIRANDIIRITOPERATESSIMPLYSINGLE,CONVENIENTANDFLEXIBLEINTHEPROCESSOFSIGNALPROCESSING,THEELIMINATIONOFNOISEISTHEMOSTBASICONETOELIMINATEORREDUCENOISEINTERFERENCE,TOIMPROVETHESIGNALTONOISERATIO,TOIMPROVETHESIGNALDETECTIONPROBABILITYISOFGREATIMPORTANCEABANDPASSFILTERISDESIGNEDINTHISPAPER,REMOVETHEGAUSSWHITENOISEANDEXTRACTTHEUSEFULSIGNALXTSIN2,81TINTHENOISYENVIRONMENT,THEFREQUENCYOFTHEFILTERMUSTBEIMPROVEDWHENTHEUSEFULSIGNALISDETECTEDRATESELECTIVE,ANDTHEBANDTOSTOPBANDATTENUATIONISFASTERTHISPAPERUSESHAMMINGWINDOWA100PASSBANDFIRDFISDESIGNEDTOACHIEVETHESAMPLINGFREQUENCYOFFS1000HZ,PASSBAND,CUTOFFFREQUENCY,FC175,HZ,ANDSTOPBANDCUTOFFFREQUENCYFC2100HZ,ANDTHESPECIFICPARAMETERSARESHOWNINFIGURE2WHENTHEMAINLOBEISNARROWER,THEHIGHERTHEORDER,THEBETTERABALANCEBETWEENTHETWOINTHEDESIGNAVOIDWASTEOFRESOURCES2MODELINGANDSIMULATIONOFSIMULINKENVIRONMENTFIRBANDPASSFILTERISTESTEDBYSIMULATIONTESTINSIMULINKENVIRONMENTABILITYTODENOISECALLTHEFUNCTIONALMODULESINSIMULINKTOFORMADIGITALFILTERTHESIMULATIONBLOCKDIAGRAMOFWAVECONVERTER,INTHEPROCESSOFSIMULATION,YOUCANDOUBLECLICKEACHFUNCTIONMODULEWHENTHEPARAMETERSARECHANGED,THESIMULATIONRESULTSUNDERDIFFERENTCONDITIONSAREOBTAINEDTHESIMULATIONFIGUREISSHOWNINFIGURE3ASSHOWN67THIRTYTHIRDROLLSOFELECTRICITYFIGURE2BANDPASSFIRDFDESIGNFIG3FIRBANDPASSFILTERSIMULINKSIMULATIONINTHESIMULINKENVIRONMENT,AFTERSETTINGUPTHEMODELOFTHEFIRFILTER,USETHESINEWAVEGENERATINGMODULEGENERATESASIGNALOFXTSIN2,81T,ANDTHENTHESIGNALPROCESSINGSOURCESTOOLBOXINVOKESTHERANDOMSOURCEMODULEBLOCKSAREUSEDTOGENERATEGAUSSWHITENOISEANDIMPORT12DESIGNEDFILTERSTHEFILTERDESIGNMODULETAKESADVANTAGEOFTHESCOPEANDSPECTRUMSCOPEMODULESWAVEFORMSINTIMEANDFREQUENCYDOMAINSARESHOWNWHENYOUREDONE,CLICKTHESTARTBUTTONTOFILTERTHEWAVEFORMCONTRASTBEFOREANDAFTERTHEWAVEISSHOWNINFIGURE4TIMEDOMAINWAVEFORMCONTRASTCHART,SUCHASASSHOWNINFIGURE5FROMTHESIMULATIONRESULTS,THESIGNALSCANHARDLYDISTINGUISHTHEUSEFULSIGNALSFROMTHEOTHERSAFTERTHENOISESIGNALISFILTERED,THENOISESIGNALISEFFECTIVELYSUPPRESSEDANDIMPROVEDWITHTHEDETECTIONPROBABILITYOFSIGNAL,THEEXPECTEDGOALISACHIEVEDTHESIMULATIONTESTCANBEDONEBYSIMULATIONTHEFILTERPERFORMANCEOFTHEREALTESTFILTERISCHOSEN,ANDDIFFERENTTRANSMISSIONISCHOSENACCORDINGTOTHEACTUALSITUATIONTOANALYZEANDCOMPARETHESIGNALBEFOREANDAFTERFILTERINGTOIMPROVETHESITUATIONCHENGYINGYONGPROVIDESSTRONGEVIDENCEFIG4COMPARISONOFWAVEFORMINFREQUENCYDOMAINBEFOREANDAFTERFILTERING68MAYUEHONG,ETCMATLABBASEDFIRDIGITALFILTERDESIGNANDSIMULATIONOFTHEELEVENTHPHASEFIG5COMPARISONOFTIMEDOMAINWAVEFORMBEFOREANDAFTERFILTERING3CONCLUSIONADIGITALFILTERDESIGNMETHODUSINGMATLABSIGNALPROCESSINGTOOLBOXCANBEUSEDITISCONVENIENTTODESIGNACONVENTIONALDIGITALFILTERWHICHISCOMPOSEDOFSOFTWARE,FAST,GREATLYREDUCINGTHEWORKLOADINTHEDESIGNPROCESS,CONTRASTFILTERSCANBEUSEDTHEPARAMETERSARECHANGEDATANYTIME,ANDTHEPERFORMANCEOFEACHFILTERISSIMULATEDTOACHIEVEFILTERINGTHEOPTIMALDESIGNOFTHEDEVICEISDESIGNEDTOPROVIDERELIABLESUPPORTFORTHEREASONABLEAPPLICATIONOFTHEFILTERITHELPSTOIMPROVETHEABILITYOFENGINEERINGTECHNICIANSTOANALYZEANDSOLVEPROBLEMSREFERENCE1WANGJUNWEI,RENHANFIRDIGITALFILTERBASEDONFREQUENCYSAMPLINGTECHNIQUEOPTIMUMDESIGNOFWAVEINSTRUMENTJ,PROCEEDINGSOFTHEINSTITUTEOFINSTRUMENTATION,2005,2684754772ZHANGPINGFIRDIGITALFILTERBASEDONMATLABANDDSPDESIGNJCHINESESCIENCEANDTECHNOLOGYINFORMATION,20072380813DINGLEI,PANZHENCUN,CONGWEIBASEDONMATLABSIGNALPROCESSINGTOOLBOXDESIGNANDSIMULATIONOFDIGITALFILTERSJ,RELAYS,2003,31948514YANGCOLUMNTHEDESIGNANDSIMULATIONOFFIRFILTERMATLABENVIRONMENTJAPPLICATIONOFELECTRONICTECHNOLOGY,200691011035,YANXIAOYAN,FUFENGLIN,CHENJIAN,ETALFIRDIGITALFILTERDESIGNANDSIMULATIONIMPLEMENTATIONINMATLABJELECTRONICTECHNOLOGY,2004,517643466SONG,CHEN,ZHAOZHIMINFASTFOURIERTRANSFORMAIDEDDESIGN,DIGITALLOWPASSFILTERJOPTOELECTRONICSLASERS,2007,1018116911727H,AN,K,H,KIM,J,H,QUANTUMINSPIRED,EVO,LUTIO,NAR,YALG,OR,ITHM,FOR,A,CLASS,OF,COMBINATIONAL,O,PT,IMIZATIONJIEEE,T,RANS,ON,EVO,LNTIO,NAR,COMPUTATION,Y,2002,665808938H,EY,T,QUANTUM,COM,PUTING,AN,INTR,ODUCTION,JCOMPUTING,CONTR,OL,ENG,INEERING,JO,UR,NAL,1999,103105112BRIEFINTRODUCTIONOFTHEAUTHORHONGHONG,FEMALE,BORNINMARCH1979,M