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

IIRDIGITALFILTERDESIGN作者SANJITKMITRA国籍USA出处DIGITALSIGNALPROCESSINGACOMPUTERBASEDAPPROACH3EANIMPORTANTSTEPINTHEDEVELOPMENTOFADIGITALFILTERISTHEDETERMINATIONOFAREALIZABLETRANSFERFUNCTIONGZAPPROXIMATINGTHEGIVENFREQUENCYRESPONSESPECIFICATIONSIFANIIRFILTERISDESIRED,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,PPJPFOREG,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,THESEPCIFIEDCRITICALPSFREQUENCIESNEEDTOBENORMALIZEDBEFOREASPECIFICF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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