matlab 滤波器 外文翻译 外文文献 英文文献 iir数字滤波器的设计

IIRDIGITALFILTERDESIGNANIMPORTANTSTEPINTHEDEVELOPMENTOFADIGITALFILTERISTHEDETERMINATIONOFAREALIZABLETRANSFERFUNCTIONGZAPPROXIMATINGTHEGIVENFREQUENCYRESPONSESPECIFICATIONSIFANIIRFILTERISDESIRED,ITISALSONECESSARYTOENSURETHATGZISSTABLETHEPROCESSOFDERIVINGTHETRANSFERFUNCTIONGZISCALLEDDIGITALFILTERDESIGNAFTERGZHASBEENOBTAINED,THENEXTSTEPISTOREALIZEITINTHEFORMOFASUITABLEFILTERSTRUCTUREINCHAPTER8,WEOUTLINEDAVARIETYOFBASICSTRUCTURESFORTHEREALIZATIONOFFIRANDIIRTRANSFERFUNCTIONSINTHISCHAPTER,WECONSIDERTHEIIRDIGITALFILTERDESIGNPROBLEMTHEDESIGNOFFIRDIGITALFILTERSISTREATEDINCHAPTER10FIRSTWEREVIEWSOMEOFTHEISSUESASSOCIATEDWITHTHEFILTERDESIGNPROBLEMAWIDELYUSEDAPPROACHTOIIRFILTERDESIGNBASEDONTHECONVERSIONOFAPROTOTYPEANALOGTRANSFERFUNCTIONTOADIGITALTRANSFERFUNCTIONISDISCUSSEDNEXTTYPICALDESIGNEXAMPLESAREINCLUDEDTOILLUSTRATETHISAPPROACHWETHENCONSIDERTHETRANSFORMATIONOFONETYPEOFIIRFILTERTRANSFERFUNCTIONINTOANOTHERTYPE,WHICHISACHIEVEDBYREPLACINGTHECOMPLEXVARIABLEZBYAFUNCTIONOFZFOURCOMMONLYUSEDTRANSFORMATIONSARESUMMARIZEDFINALLYWECONSIDERTHECOMPUTERAIDEDDESIGNOFIIRDIGITALFILTERTOTHISEND,WERESTRICTOURDISCUSSIONTOTHEUSEOFMATLABINDETERMININGTHETRANSFERFUNCTIONS91PRELIMINARYCONSIDERATIONSTHEREARETWOMAJORISSUESTHATNEEDTOBEANSWEREDBEFOREONECANDEVELOPTHEDIGITALTRANSFERFUNCTIONGZTHEFIRSTANDFOREMOSTISSUEISTHEDEVELOPMENTOFAREASONABLEFILTERFREQUENCYRESPONSESPECIFICATIONFROMTHEREQUIREMENTSOFTHEOVERALLSYSTEMINWHICHTHEDIGITALFILTERISTOBEEMPLOYEDTHESECONDISSUEISTODETERMINEWHETHERANFIRORIIRDIGITALFILTERISTOBEDESIGNEDINTHESECTION,WEEXAMINETHESETWOISSUESFIRSTNEXTWEREVIEWTHEBASICANALYTICALAPPROACHTOTHEDESIGNOFIIRDIGITALFILTERSANDTHENCONSIDERTHEDETERMINATIONOFTHEFILTERORDERTHATMEETSTHEPRESCRIBEDSPECIFICATIONSWEALSODISCUSSAPPROPRIATESCALINGOFTHETRANSFERFUNCTION911DIGITALFILTERSPECIFICATIONSASINTHECASEOFTHEANALOGFILTER,EITHERTHEMAGNITUDEAND/ORTHEPHASEDELAYRESPONSEISSPECIFIEDFORTHEDESIGNOFADIGITALFILTERFORMOSTAPPLICATIONSINSOMESITUATIONS,THEUNITSAMPLERESPONSEORSTEPRESPONSEMAYBESPECIFIEDINMOSTPRACTICALAPPLICATIONS,THEPROBLEMOFINTERESTISTHEDEVELOPMENTOFAREALIZABLEAPPROXIMATIONTOAGIVENMAGNITUDERESPONSESPECIFICATIONASINDICATEDINSECTION463,THEPHASERESPONSEOFTHEDESIGNEDFILTERCANBECORRECTEDBYCASCADINGITWITHANALLPASSSECTIONTHEDESIGNOFALLPASSPHASEEQUALIZERSHASRECEIVEDAFAIRAMOUNTOFATTENTIONINTHELASTFEWYEARSWERESTRICTOURATTENTIONINTHISCHAPTERTOTHEMAGNITUDEAPPROXIMATIONPROBLEMONLYWEPOINTEDOUTINSECTION441THATTHEREAREFOURBASICTYPESOFFILTERS,WHOSEMAGNITUDERESPONSESARESHOWNINFIGURE410SINCETHEIMPULSERESPONSECORRESPONDINGTOEACHOFTHESEISNONCAUSALANDOFINFINITELENGTH,THESEIDEALFILTERSARENOTREALIZABLEONEWAYOFDEVELOPINGAREALIZABLEAPPROXIMATIONTOTHESEFILTERWOULDBETOTRUNCATETHEIMPULSERESPONSEASINDICATEDINEQ472FORALOWPASSFILTERTHEMAGNITUDERESPONSEOFTHEFIRLOWPASSFILTEROBTAINEDBYTRUNCATINGTHEIMPULSERESPONSEOFTHEIDEALLOWPASSFILTERDOESNOTHAVEASHARPTRANSITIONFROMPASSBANDTOSTOPBANDBUT,RATHER,EXHIBITSAGRADUAL“ROLLOFF“THUS,ASINTHECASEOFTHEANALOGFILTERDESIGNPROBLEMOUTLINEDINSECTION541,THEMAGNITUDERESPONSESPECIFICATIONSOFADIGITALFILTERINTHEPASSBANDANDINTHESTOPBANDAREGIVENWITHSOMEACCEPTABLETOLERANCESINADDITION,ATRANSITIONBANDISSPECIFIEDBETWEENTHEPASSBANDANDTHESTOPBANDTOPERMITTHEMAGNITUDETODROPOFFSMOOTHLYFOREXAMPLE,THEMAGNITUDEOFALOWPASSFILTERMAYBEGIVENASSHOWNINFIGUREJEG71ASINDICATEDINTHEFIGURE,INTHEPASSBANDDEFINEDBY0,WEREQUIRETHATTHEPMAGNITUDEAPPROXIMATESUNITYWITHANERROROF,IE,PPPJPFOREG,11INTHESTOPBAND,DEFINEDBY,WEREQUIRETHATTHEMAGNITUDEAPPROXIMATESZEROSWITHANERROROFE,IS,FOR,SJESTHEFREQUENCIESANDARE,RESPECTIVELY,CALLEDTHEPASSBANDEDGEFREQUENCYANDTHEPSSTOPBANDEDGEFREQUENCYTHELIMITSOFTHETOLERANCESINTHEPASSBANDANDSTOPBAND,PAND,AREUSUALLYCALLEDTHEPEAKRIPPLEVALUESNOTETHATTHEFREQUENCYRESPONSESOFADIGITALFILTERISAPERIODICFUNCTIONOF,ANDTHEMAGNITUDERESPONSEOFAREALJEGCOEFFICIENTDIGITALFILTERISANEVENFUNCTIONOFASARESULT,THEDIGITALFILTERSPECIFICATIONSAREGIVENONLYFORTHERANGE0DIGITALFILTERSPECIFICATIONSAREOFTENGIVENINTERMSOFTHELOSSFUNCTION,INDBHERETHEPEAKPASSBANDRIPPLEANDTHEMINIMUMLOG201JEGPSTOPBANDATTENUATIONAREGIVENINDB,IE,THELOSSSPECIFICATIONSOFADIGITALFILTERARESGIVENBY,DBPP1LOG20SS091PRELIMINARYCONSIDERATIONSASINTHECASEOFANANALOGLOWPASSFILTER,THESPECIFICATIONSFORADIGITALLOWPASSFILTERMAYALTERNATIVELYBEGIVENINTERMSOFITSMAGNITUDERESPONSE,ASINFIGURE72HERETHEMAXIMUMVALUEOFTHEMAGNITUDEINTHEPASSBANDISASSUMEDTOBEUNITY,ANDTHEMAXIMUMPASSBANDDEVIATION,DENOTEDAS1/,ISGIVENBYTHEMINIMUMVALUEOF21THEMAGNITUDEINTHEPASSBANDTHEMAXIMUMSTOPBANDMAGNITUDEISDENOTEDBY1/AFORTHENORMALIZEDSPECIFICATION,THEMAXIMUMVALUEOFTHEGAINFUNCTIONORTHEMINIMUMVALUEOFTHELOSSFUNCTIONISTHEREFORE0DBTHEQUANTITYGIVENBYMAXDB1LOG202MAXISCALLEDTHEMAXIMUMPASSBANDATTENUATIONFOR1,ASISTYPICALLYTHECASE,ITPCANBESHOWNTHATP21LOG20MAXTHEPASSBANDANDSTOPBANDEDGEFREQUENCIES,INMOSTAPPLICATIONS,ARESPECIFIEDINHZ,ALONGWITHTHESAMPLINGRATEOFTHEDIGITALFILTERSINCEALLFILTERDESIGNTECHNIQUESAREDEVELOPEDINTERMSOFNORMALIZEDANGULARFREQUENCIESAND,THESEPCIFIEDCRITICALPSFREQUENCIESNEEDTOBENORMALIZEDBEFOREASPECIFICFILTERDESIGNALGORITHMCANBEAPPLIEDLETDENOTETHESAMPLINGFREQUENCYINHZ,ANDFPANDFSDENOTE,RESPECTIVELY,THETFPASSBANDANDSTOPBANDEDGEFREQUENCIESINHZTHENTHENORMALIZEDANGULAREDGEFREQUENCIESINRADIANSAREGIVENBYTFPTP2FSSS912SELECTIONOFTHEFILTERTYPETHESECONDISSUEOFINTERESTISTHESELECTIONOFTHEDIGITALFILTERTYPE,IE,WHETHERANIIRORANFIRDIGITALFILTERISTOBEEMPLOYEDTHEOBJECTIVEOFDIGITALFILTERDESIGNISTODEVELOPACAUSALTRANSFERFUNCTIONHZMEETINGTHEFREQUENCYRESPONSESPECIFICATIONSFORIIRDIGITALFILTERDESIGN,THEIIRTRANSFERFUNCTIONISAREALRATIONALFUNCTIONOF1ZHZNMDZZDPP210MOREOVER,HZMUSTBEASTABLETRANSFERFUNCTION,ANDFORREDUCEDCOMPUTATIONALCOMPLEXITY,ITMUSTBEOFLOWESTORDERNONTHEOTHERHAND,FORFIRFILTERDESIGN,THEFIRTRANSFERFUNCTIONISAPOLYNOMIALIN1ZNNNZHZH0FORREDUCEDCOMPUTATIONALCOMPLEXITY,THEDEGREENOFHZMUSTBEASSMALLASPOSSIBLEINADDITION,IFALINEARPHASEISDESIRED,THENTHEFIRFILTERCOEFFICIENTSMUSTSATISFYTHECONSTRAINTNHTHEREARESEVERALADVANTAGESINUSINGANFIRFILTER,SINCEITCANBEDESIGNEDWITHEXACTLINEARPHASEANDTHEFILTERSTRUCTUREISALWAYSSTABLEWITHQUANTIZEDFILTERCOEFFICIENTSHOWEVER,INMOSTCASES,THEORDERNFIROFANFIRFILTERISCONSIDERABLYHIGHERTHANTHEORDERNIIROFANEQUIVALENTIIRFILTERMEETINGTHESAMEMAGNITUDESPECIFICATIONSINGENERAL,THEIMPLEMENTATIONOFTHEFIRFILTERREQUIRESAPPROXIMATELYNFIRMULTIPLICATIONSPEROUTPUTSAMPLE,WHEREASTHEIIRFILTERREQUIRES2NIIR1MULTIPLICATIONSPEROUTPUTSAMPLEINTHEFORMERCASE,IFTHEFIRFILTERISDESIGNEDWITHALINEARPHASE,THENTHENUMBEROFMULTIPLICATIONSPEROUTPUTSAMPLEREDUCESTOAPPROXIMATELYNFIR1/2LIKEWISE,MOSTIIRFILTERDESIGNSRESULTINTRANSFERFUNCTIONSWITHZEROSONTHEUNITCIRCLE,ANDTHECASCADEREALIZATIONOFANIIRFILTEROFORDERWITHALLOFTHEZEROSONTHEUNITIRNCIRCLEREQUIRES33/2MULTIPLICATIONSPEROUTPUTSAMPLEITHASBEENSHOWNTHATIRNFORMOSTPRACTICALFILTERSPECIFICATIONS,THERATIONFIR/NIIRISTYPICALLYOFTHEORDEROFTENSORMOREAND,ASARESULT,THEIIRFILTERUSUALLYISCOMPUTATIONALLYMOREEFFICIENTRAB75HOWEVER,IFTHEGROUPDELAYOFTHEIIRFILTERISEQUALIZEDBYCASCADINGITWITHANALLPASSEQUALIZER,THENTHESAVINGSINCOMPUTATIONMAYNOLONGERBETHATSIGNIFICANTRAB75INMANYAPPLICATIONS,THELINEARITYOFTHEPHASERESPONSEOFTHEDIGITALFILTERISNOTANISSUE,MAKINGTHEIIRFILTERPREFERABLEBECAUSEOFTHELOWERCOMPUTATIONALREQUIREMENTS913BASICAPPROACHESTODIGITALFILTERDESIGNINTHECASEOFIIRFILTERDESIGN,THEMOSTCOMMONPRACTICEISTOCONVERTTHEDIGITALFILTERSPECIFICATIONSINTOANALOGLOWPASSPROTOTYPEFILTERSPECIFICATIONS,ANDTHENTOTRANSFORMITINTOTHEDESIREDDIGITALFILTERTRANSFERFUNCTIONGZTHISAPPROACHHASBEENWIDELYUSEDFORMANYREASONSAANALOGAPPROXIMATIONTECHNIQUESAREHIGHLYADVANCEDBTHEYUSUALLYYIELDCLOSEDFORMSOLUTIONSCEXTENSIVETABLESAREAVAILABLEFORANALOGFILTERDESIGNDMANYAPPLICATIONSREQUIRETHEDIGITALSIMULATIONOFANALOGFILTERSINTHESEQUEL,WEDENOTEANANALOGTRANSFERFUNCTIONAS,SDPHAAWHERETHESUBSCRIPT“A“SPECIFICALLYINDICATESTHEANALOGDOMAINTHEDIGITALTRANSFERFUNCTIONDERIVEDFORMHASISDENOTEDBYZPGTHEBASICIDEABEHINDTHECONVERSIONOFANANALOGPROTOTYPETRANSFERFUNCTIONHASINTOADIGITALIIRTRANSFERFUNCTIONGZISTOAPPLYAMAPPINGFROMTHESDOMAINTOTHEZDOMAINSOTHATTHEESSENTIALPROPERTIESOFTHEANALOGFREQUENCYRESPONSEAREPRESERVEDTHEIMPLIESTHATTHEMAPPINGFUNCTIONSHOULDBESUCHTHATATHEIMAGINARYJAXISINTHESPLANEBEMAPPEDONTOTHECIRCLEOFTHEZPLANEBASTABLEANALOGTRANSFERFUNCTIONBETRANSFORMEDINTOASTABLEDIGITALTRANSFERFUNCTIONTOTHISEND,THEMOSTWIDELYUSEDTRANSFORMATIONISTHEBILINEARTRANSFORMATIONDESCRIBEDINSECTION92UNLIKEIIRDIGITALFILTERDESIGN,THEFIRFILTERDESIGNDOESNOTHAVEANYCONNECTIONWITHTHEDESIGNOFANALOGFILTERSTHEDESIGNOFFIRFILTERDESIGNDOESNOTHAVEANYCONNECTIONWITHTHEDESIGNOFANALOGFILTERSTHEDESIGNOFFIRFILTERSISTHEREFOREBASEDONADIRECTAPPROXIMATIONOFTHESPECIFIEDMAGNITUDERESPONSE,WITHTHEOFTENADDEDREQUIREMENTTHATTHEPHASERESPONSEBELINEARASPOINTEDOUTINEQ710,ACAUSALFIRTRANSFERFUNCTIONHZOFLENGTHN1ISAPOLYNOMIALINZ1OFDEGREENTHECORRESPONDINGFREQUENCYRESPONSEISGIVENBYNNNJJEHEH0ITHASBEENSHOWNINSECTION321THATANYFINITEDURATIONSEQUENCEXNOFLENGTHN1ISCOMPLETELYCHARACTERIZEDBYN1SAMPLESOFITSDISCRETETIMEFOURIERTRANSFERXASAJERESULT,THEDESIGNOFANFIRFILTEROFLENGTHN1MAYBEACCOMPLISHEDBYFINDINGEITHERTHEIMPULSERESPONSESEQUENCEHNORN1SAMPLESOFITSFREQUENCYRESPONSEALSO,HJTOENSUREALINEARPHASEDESIGN,THECONDITIONOFEQ711MUSTBESATISFIEDTWODIRECTAPPROACHESTOTHEDESIGNOFFIRFILTERSARETHEWINDOWEDFOURIERSERIESAPPROACHANDTHEFREQUENCYSAMPLINGAPPROACHWEDESCRIBETHEFORMERAPPROACHINSECTION76THESECONDAPPROACHISTREATEDINPROBLEM76INSECTION77WEOUTLINECOMPUTERBASEDDIGITALFILTERDESIGNMETHODS作者SANJITKMITRA国籍USA出处DIGITALSIGNALPROCESSINGACOMPUTERBASEDAPPROACH3EIIR数字滤波器的设计在一个数字滤波器发展的重要步骤是可实现的传递函数G（Z）的接近给定的频率响应规格。如果一个IIR滤波器是理想，它也有必要确保了G（Z）是稳定的。该推算传递函数G（Z）的过程称为数字滤波器的设计。然后G（Z）有所值，下一步就是实现在一个合适的过滤器结构形式。在第8章，我们概述了为转移的FIR和IIR的各种功能的实现基本结构。在这一章中，我们考虑的IIR数字滤波器的设计问题。FIR数字滤波器的设计是在第10章处理。首先，我们回顾与滤波器设计问题相关的一些问题。一种广泛使用的方法来设计IIR滤波器的基础上，传递函数原型模拟到数字的转换传递函数进行了讨论下一步。典型的设计实例来说明这种方法。然后，我们考虑到另一种类型，它是由一个函数代替复杂的变量Z达到了一个IIR滤波器的传递函数Z的类型转换四种常用的转换进行了总结。最后，我们考虑的IIR计算机辅助设计数字滤波器。为此，我们限制我们讨论了MATLAB在确定传递函数的使用。91初步考虑有两个需要先有一个回答可以发展数字传递函数G（Z）的重大问题。首要的问题是一个合理的滤波器的频率响应规格从整个系统中数字滤波器将被雇用的要求发展。第二个问题是要确定的FIR或IIR数字滤波器是设计。在一节中，我们首先检查了这两个问题。接下来，我们回顾到的IIR数字滤波器设计的基本分析方法，然后再考虑过滤器的顺序符合规定的规格测定。我们还讨论了传递函数适当的调整。911数字过滤器的规格如过滤器的模拟案件，无论是规模和/或相位（延迟）响应对于大多数应用程序指定一个数字滤波器FORTHE设计。在某些情况下，单位采样响应或阶跃响应可能被指定。在大多数实际应用中，利益问题是一个变现逼近一个给定的幅度响应的规范发展。如第463所示，所设计的滤波器可以通过级联与全通区段纠正相位响应。全通相位均衡器的设计接受了最近几年，相当数量的关注。我们在这方面限制的幅度逼近问题的唯一一章我们的注意。我们指出，在第441节指出，有四个过滤器，其大小，如图410所示的反应基本类型。由于脉冲响应对应于所有这些都是非因果和无限长，这些过滤器是尚未实现的理想。一个发展一个变现的近似值，这些过滤器的方法是截断的脉冲响应，如式所示。（472）为低通滤波器。该FIR低幅度响应滤波器得到截断的理想低通滤波器，从没有一个通带过渡到阻带尖脉冲响应，而是呈现出逐步“滚降。”因此，正如在模拟滤波器设计541节中所述的问题情况下，在通带数字滤波器和阻带幅频响应规格给予一些可接受的公差。此外，指定一个过渡带之间的通带和阻带允许的幅度下降顺利。例如，一个低通滤波器的幅度可能得到如图71所示。正如在图中定义的通带0，我们要求的幅度接近同一个，即错误的团结，。在界定的阻带，我们要求的幅度接近零与一的错误。大肠杆菌，为。的频率，并分别被称为通带边缘频率和阻带边缘频率。在通带和阻带，并且，公差的限制，通常称为峰值纹波值。请注意，数字滤波器的频率响应是周期函数，以及幅度响应的实时数字滤波器系数是一个偶函数的。因此，数字滤波规格只给出了范围。数字滤波器的规格，常常给在功能上的损失分贝，。在这里，通带纹波和峰值最小阻带衰减给出了分贝，也就是说，数字滤波器，给出的损失规格，。91初步设想正如在一个模拟低通滤波器的情况下，一个数字低通滤波器的规格可能或者给予其规模在反应方面，如图72。在这里，在通带内规模最大的价值被假定为团结，最大通带偏差，表示为1/，是由通带中的最低值所规模。阻带的最大震级是指由1/答对于标准化规格，增益功能或损失函数的最小值最大值，因此分贝。给予的数量被称为最大通带衰减。1，由于通常情况下，它可以证明通带和阻带边缘频率在大多数应用中，被指定为HZ，随着数字滤波器的采样率。由于所有的过滤器设计技术的规范化发展和角频率来看，临界频率的SEPCIFIED之前需要一个特定的过滤器设计算法可以应用于正常化。让表示，在赫兹采样频率，计划生育和FS分别表示，在通带和阻带的边缘在赫兹频率。然后正常化弧度角频率都是通过边912过滤器类型的选择利息的第二个问题是数字滤波器的类型，即选择，无论是原居民或FIR数字滤波器将被雇用。数字滤波器的设计目标是建立一个因果传递函数H（Z）的频率响应规格会议。对于IIR数字滤波器的设计，即原传递函数是一个真正合理的功能。的H（Z）的此外，高（Z）的必须是一个稳定的传输功能，并减少了计算的复杂性，它必须以最低的全是另一方面，对FIR滤波器的设计，区传递函数是一个多项式为了降低计算复杂度，N次的H（Z）的，必须尽可能的小。此外，如果是理想的线性相位，然后将FIR滤波器系数必须满足的约束所以采用FIR滤波器的几个优点，因为它可以被设计成精确线性相位滤波器的结构和量化滤波器系数总是与稳定。然而，在大多数情况下，为了NFIR一个FIR滤波器是大大高于同等IIR滤波器会议同样大小的规格为NIIR高。在一般情况下，FIR滤波器的实现需要每个输出样本约NFIR乘法，而每IIR滤波器2NIIR一输出示例乘法要求。在前者情况下，如果FIR滤波器的设计与线性阶段，那么每个输出的采样乘法次数减少到大约（NFIR1）/2。同样，多数IIR滤波器的设计结果与单位圆上的传递函数零，而级联的IIR滤波器实现秩序与单位圆上的零点都需要（33）/2乘法每个输出样本。它已被证明是最实用的过滤器的规格，比NFIR/NIIR通常为几十或更多的订单，并作为结果，计算IIR滤波器通常是更有效RAB75。但是，如果IIR滤波器的群延迟是由全通均衡器级联与它扳平，然后在计算储蓄可能不再是显着RAB75。在许多应用中，该数字滤波器的相位响应线性不是问题，使IIR滤波器因为较低的计算要求可取。913数字滤波器设计的基本方法在IIR滤波器的设计中，最常见的做法是将其转换成模拟低通原型滤波器规格的数字过滤器的规格，然后转换成所需的数字滤波器的传递函数的G（Z）的。这种方法已广泛应用于许多原因（A）模拟技术是非常先进的逼近。（B）他们通常产量封闭形式的解决方案。（C）广泛用于模拟表滤波器设计提供。（D）许多应用需要模拟滤波器数字仿真。在续集中，我们记一个模拟的传递函数为，其中，下标“一”明确表示模拟域。数字传递函数导出的形式下（S）是由记背后的传递函数模拟原型哈（S）转换成数字原居民的基本思想传递函数G（Z）是一个适用于从S域映射到Z域，使模拟频率的基本属性响应将被保留。在暗示，映射函数应该是这样的虚（J）在S平面轴映射到的Z平面圆。一个稳定的信号传递函数转化为一个稳定的数字传输功能。为此，使用最广泛的变革是双线性变换在92节中所述。不像IIR数字滤波器设计，FIR滤波器的设计没有任何的模拟滤波器的设计连接。作者SANJITKMITRA国籍USA出处DIGITALSIGNALPROCESSINGACOMPUTERBASEDAPPROACH3EFIRDIGITALFILTERDESIGNINCHAPTER9WECONSIDEREDTHEDESIGNOFIIRDIGITALFILTERSFORSUCHFILTERS,ITISALSONECESSARYTOENSURETHATTHEDERIVEDTRANSFERFUNCTIONGZISSTABLEONTHEOTHERHAND,INTHECASEOFFIRDIGITALFILTERDESIGN,THESTABILITYISNOTADESIGNISSUEASTHETRANSFERFUNCTIONISAPOLYNOMIALINZ1ANDISTHUSALWAYSGUARANTEEDSTABLEINTHISCHAPTER,WECONSIDERTHEFIRDIGITALFILTERDESIGNPROBLEMUNLIKETHEIIRDIGITALFILTERDESIGNPROBLEM,ITISALWAYSPOSSIBLETODESIGNFIRDIGITALFILTERSWITHEXACTLINEARPHASEFIRST,WEDESCRIBEAPOPULARAPPROACHTOTHEDESIGNOFFIRDIGITALFILTERSWITHLINEARPHASEWETHENCONSIDERTHECOMPUTERAIDEDDESIGNOFLINEARPHASEFIRDIGITALFILTERSTOTHISEND,WERESTRICTOURDISCUSSIONTOTHEUSEOFMATLABINDETERMININGTHETRANSFERFUNCTIONSSINCETHEORDEROFTHEFIRTRANSFERFUNCTIONISUSUALLYMUCHHIGHERTHANTHATOFANIIRTRANSFERFUNCTIONMEETINGTHESAMEFREQUENCYRESPONSESPECIFICATIONS,WEOUTLINETWOMETHODSFORTHEDESIGNOFCOMPUTATIONALLYEFFICIENTFIRDIGITALFILTERSREQUIRINGFEWERMULTIPLIERSTHANADIRECTFORMREALIZATIONFINALLY,WEPRESENTAMETHODOFDESIGNINGAMINIMUMPHASEFIRDIGITALFILTERTHATLEADSTOATRANSFERFUNCTIONWITHSMALLERGROUPDELAYTHANTHATOFALINEARPHASEEQUIVALENTTHEMINIMUMPHASEFIRDIGITALFILTERISTHUSATTRACTIVEINAPPLICATIONSWHERETHELINEARPHASEREQUIREMENTISNOTANISSUE101PRELIMINARYCONSIDERATIONSINTHISSECTION,WEFIRSTREVIEWSOMEBASICAPPROACHESTOTHEDESIGNOFFIRDIGITALFILTERSANDTHEDETERMINATIONOFTHEFILTERORDERTOMEETTHEPRESCRIBEDSPECIFICATIONS1011BASICAPPROACHESTOFIRDIGITALFILTERDESIGNUNLIKEIIRDIGITALFILTERDESIGN,FIRFILTERDESIGNDOESNOTHAVEANYCONNECTIONWITHTHEDESIGNOFANALOGFILTERSTHEDESIGNOFFIRFILTERSISTHEREFOREBASEDONADIRECTAPPROXIMATIONOFTHESPECIFIEDMAGNITUDERESPONSE,WITHTHEOFTENADDEDREQUIREMENTTHATTHEPHASERESPONSEBELINEARRECALLACAUSALFIRTRANSFERFUNCTIONHZOFLENGTHN1ISAPOLYNOMIALINZ1OFDEGREEN101NNNZHZH0THECORRESPONDINGFREQUENCYRESPONSEISGIVENBY102NNNJJEE0ITHASBEENSHOWNINSECTION531THATANYFINITEDURATIONSEQUENCEXNOFLENGTHN1ISCOMPLETELYCHARACTERIZEDBYN1SAMPLESOFITSDISCRETETIMEFOURIERTRANSFORMXASAJERESULT,THEDESIGNOFANFIRFILTEROFLENGTHN1CANBEACCOMPLISHEDBYFINDINGEITHERTHEIMPULSERESPONSESEQUENCEHNORN1SAMPLESOFITSFREQUENCYRESPONSEHALSO,TOJENSUREALINEARPHASEDESIGN,THECONDITION,NNHMUSTBESATISFIEDTWODIRECTAPPROACHESTOTHEDESIGNOFFIRFILTERSARETHEWINDOWEDFOURIERSERIESAPPROACHANDTHEFREQUENCYSAMPLINGAPPROACHWEDESCRIBETHEFORMERAPPROACHINSECTION102THESECONDAPPROACHISTREATEDINPROBLEMS1031AND1032INSECTION103,WEOUTLINECOMPUTERBASEDDIGITALFILTERDESIGNMETHODS1012ESTIMATIONOFTHEFILTERORDERAFTERTHETYPEOFTHEDIGITALFILTERHASSELECTED,THENEXTSTEPINTHEFILTERDESIGNPROCESSISTOESTIMATETHEFILTERORDERSHOULDBETHESMALLESTINTEGERGREATERTHANOREQUALTOTHEESTIMATEDVALUEFIRDIGITALFILTERORDERESTIMATIONFORTHEDESIGNOFLOWPASSFIRDIGITALFILTERS,SEVERALAUTHORSHAVEADVANCEDFORMULASFORESTIMATINGTHEMINIMUMVALUEOFTHEFILTERORDERNDIRECTLYFROMTHEDIGITALFILTERSPECIFICATIONSNORMALIZEDPASSBANDEDGEANGULARFREQUENCY,NORMALIZEFSTOPBANDEDGEANGULARFREQUENCYP,PEAKPASSBANDRIPPLE,ANDPEAKSTOPBANDRIPPLEWEREVIEWTHREESUCHFORMULASSPSKAISERSFORMULAARATHERSIMPLEFORMULADEVELOPEDBYKAISERKAI74ISGIVENBY2/61413LOG20PSSNWEILLUSTRATETHEAPPLICATIONOFTHEABOVEFORMULAINEXAMPLE101BELLANGERSFORMULAANOTHERSIMPLEFORMULAADVANCEDBYBELLANGERISGIVENBYBEL81101PRELIMINARYCONSIDERATIONS12/30LOG1PSSNITSAPPLICATIONISCONSIDEREDINEXAMPLE102HERMANNSFORMULATHEFORMULADUETOHERMANNETALHER73GIVESASLIGHTLYMOREACCURATEVALUEFORTHEORDERANDISGIVENBY,2/,2PPSPSFDN）（WHERE,6LOG5LOG4LOG3LOG2LOG1,1021010100AAAAAADPPSPPSPAND,LL,1010SPSPBFWITHA10005309,A2007114,A304761,A4000266,A505941,A604278,B11101217,B2051244THEFORMULAGIVENINEQ105ISVALIDFORIF,THENTHEFILTERORDERFORMULATOSPSPBEUSEDISOBTAINEDBYINTERCHANGINGANDINEQ106AAND106BSFORSMALLVALUESOFAND,ALLOFTHEABOVEFORMULASPROVIDEREASONABLYCLOSEANDPSACCURATERESULTSONTHEOTHERHAND,WHENTHEVALUESOFANDARELARGE,EQ105YIELDSAPSMOREACCURATEVALUEFORTHEORDERACOMPARISONOFFIRFILTERORDERFORMULASNOTETHATTHEFILTERORDERCOMPUTEDINEXAMPLES101,102AND103,USINGEQS103,103,AND105,RESPECTIVELY,AREALLDIFFERENTEACHOFTHESETHREEFORMULASPROVIDEONLYANESTIMATEOFTHEREQUIREDFILTERORDERTHEFREQUENCYRESPONSEOFTHEFIRFILTERDESIGNEDUSINGTHISESTIMATEDORDERMAYORMAYNOTMEETTHEGIVENSPECIFICATIONSIFTHESPECIFICATIONSARENOTMET,ITISRECOMMENDEDTHATTHEFILTERORDERBEGRADUALLYINCREASEDUNTILTHESPECIFICATIONSAREMETESTIMATIONOFTHEFIRFILTERORDERUSINGMATLABISDISCUSSEDINSECTION1051ANIMPORTANTPROPERTYOFEACHOFTHEABOVETHREEFORMULASISTHATTHEESTIMATEDFILTERORDERNOFTHEFIRFILTERISINVERSELYPROPORTIONALTOTHETRANSITIONBANDWIDTHANDDOESNOTPSDEPENDONTHEACTUALLOCATIONOFTHETRANSITIONBANDTHISIMPLIESTHATASHARPCUTOFFFIRFILTERWITHANARROWTRANSITIONBANDWOULDBEOFVERYHIGHORDER,WHEREASANFIRFILTERWITHAWIDETRANSITIONBANDWILLHAVEAVERYLOWORDERANOTHERINTERESTINGPROPERTYOFKAISERSANDBELLANGERSFORMULASISTHATTHEORDERDEPENDSONTHEPRODUCTTHISIMPLIESTHATIFTHEVALUESOFANDAREINTERCHANGED,THEORDERSPPSREMAINSTHESAMETOCOMPARETHEACCURACYOFTHETHEABOVEFORMULAS,WEESTIMATEUSINGEACHFORMULATHEORDEROFTHREELINEARPHASELOWPASSFIRFILTERSOFKNOWNORDER,BANDEDGES,ANDRIPPLESTHESPECIFICATIONSOFTHETHREEFILTERSAREASFOLLOWSFILTERNO1012,240,143750,16250SPSPFILTERNO23,1,8,7SSFILTERNO30137,40,57,340SPSPTHERESULTSAREGIVENINTABLE101EACHONEOFTHETHREEFORMULASGIVENABOVECANALSOBEUSEDTOESTIMATETHEORDEROFHIGHPASS,BANDPASS,ANDBANDSTOPFIRFILTERSINTHECASEOFTHEBANDPASSANDBANDSTOPFILTERS,THEREARETWOTRANSITIONBANDSITHASBEENFOUNDTHATHERETHEFILTERORDERBASICALLYDEPENDSONTHETRANSITIONBANDWITHTHESMALLESTWIDTHWEILLUSTRATETHEUSEOFTHEKASIERSFORMULAINESTIMATINGTHEORDEROFALINEARPHASEBANDPASSFIRFILTERINEXAMPLE104作者SANJITKMITRA国籍USA出处DIGITALSIGNALPROCESSINGACOMPUTERBASEDAPPROACH3EFIR数字滤波器的设计在第9章，我们考虑了IIR数字滤波器的设计。对于这样的过滤器，它也必须确保派生传递函数G（Z）是稳定的。另一方面，在FIR数字