外文翻译-模拟滤波器analog filters

ANALOGFILTERSBESSEL,BUTTERWORTH,CHEBYSHEV,ELLIPTIC,BILINEARTRANSFORMATION1FUNCTIONS11BILINEARBILINEARTRANSFORMATIONMETHODFORANALOGTODIGITALFILTERCONVERSIONSYNTAXZD,PD,KDBILINEARZ,P,K,FSZD,PD,KDBILINEARZ,P,K,FS,FPNUMD,DENDBILINEARNUM,DEN,FSNUMD,DENDBILINEARNUM,DEN,FS,FPAD,BD,CD,DDBILINEARA,B,C,D,FSAD,BD,CD,DDBILINEARA,B,C,D,FS,FPDESCRIPTIONTHEBILINEARTRANSFORMATIONISAMATHEMATICALMAPPINGOFVARIABLESINDIGITALFILTERING,ITISASTANDARDMETHODOFMAPPINGTHESORANALOGPLANEINTOTHEZORDIGITALPLANEITTRANSFORMSANALOGFILTERS,DESIGNEDUSINGCLASSICALFILTERDESIGNTECHNIQUES,INTOTHEIRDISCRETEEQUIVALENTSTHEBILINEARTRANSFORMATIONMAPSTHESPLANEINTOTHEZPLANEBYTHISTRANSFORMATIONMAPSTHEJAXISFROMTOREPEATEDLYAROUNDTHEUNITCIRCLEEJ,FROMTOBYBILINEARCANACCEPTANOPTIONALPARAMETERFPTHATSPECIFIESPREWARPINGFP,INHERTZ,INDICATESA“MATCH“FREQUENCY,THATIS,AFREQUENCYFORWHICHTHEFREQUENCYRESPONSESBEFOREANDAFTERMAPPINGMATCHEXACTLYINPREWARPEDMODE,THEBILINEARTRANSFORMATIONMAPSTHESPLANEINTOTHEZPLANEWITHWITHTHEPREWARPINGOPTION,BILINEARMAPSTHEJAXISFROMTOREPEATEDLYAROUNDTHEUNITCIRCLEEJ,FROMTOBYINPREWARPEDMODE,BILINEARMATCHESTHEFREQUENCY2FPINRADIANSPERSECONDINTHESPLANETOTHENORMALIZEDFREQUENCY2FP/FSINRADIANSPERSECONDINTHEZPLANETHEBILINEARFUNCTIONWORKSWITHTHREEDIFFERENTLINEARSYSTEMREPRESENTATIONSZEROPOLEGAIN,TRANSFERFUNCTION,ANDSTATESPACEFORMZEROPOLEGAINZD,PD,KDBILINEARZ,P,K,FSANDZD,PD,KDBILINEARZ,P,K,FS,FPCONVERTTHESDOMAINTRANSFERFUNCTIONSPECIFIEDBYZ,P,ANDKTOADISCRETEEQUIVALENTINPUTSZANDPARECOLUMNVECTORSCONTAININGTHEZEROSANDPOLES,KISASCALARGAIN,ANDFSISTHESAMPLINGFREQUENCYINHERTZBILINEARRETURNSTHEDISCRETEEQUIVALENTINCOLUMNVECTORSZDANDPDANDSCALARKDTHEOPTIONALMATCHFREQUENCY,FPISINHERTZANDISUSEDFORPREWARPINGTRANSFERFUNCTIONNUMD,DENDBILINEARNUM,DEN,FSANDNUMD,DENDBILINEARNUM,DEN,FS,FPCONVERTANSDOMAINTRANSFERFUNCTIONGIVENBYNUMANDDENTOADISCRETEEQUIVALENTROWVECTORSNUMANDDENSPECIFYTHECOEFFICIENTSOFTHENUMERATORANDDENOMINATOR,RESPECTIVELY,INDESCENDINGPOWERSOFSLETBSBETHENUMERATORPOLYNOMIALANDASBETHEDENOMINATORPOLYNOMIALTHETRANSFERFUNCTIONISFSISTHESAMPLINGFREQUENCYINHERTZBILINEARRETURNSTHEDISCRETEEQUIVALENTINROWVECTORSNUMDANDDENDINDESCENDINGPOWERSOFZASCENDINGPOWERSOFZ1FPISTHEOPTIONALMATCHFREQUENCY,INHERTZ,FORPREWARPINGSTATESPACEAD,BD,CD,DDBILINEARA,B,C,D,FSANDAD,BD,CD,DDBILINEARA,B,C,D,FS,FPCONVERTTHECONTINUOUSTIMESTATESPACESYSTEMINMATRICESA,B,C,DTOTHEDISCRETETIMESYSTEMFSISTHESAMPLINGFREQUENCYINHERTZBILINEARRETURNSTHEDISCRETEEQUIVALENTINMATRICESAD,BD,CD,DDTHEOPTIONALMATCHFREQUENCY,FPISINHERTZANDISUSEDFORPREWARPINGDIAGNOSTICSBILINEARREQUIRESTHATTHENUMERATORORDERBENOGREATERTHANTHEDENOMINATORORDERIFTHISISNOTTHECASE,BILINEARDISPLAYSNUMERATORCANNOTBEHIGHERORDERTHANDENOMINATORFORBILINEARTODISTINGUISHBETWEENTHEZEROPOLEGAINANDTRANSFERFUNCTIONLINEARSYSTEMFORMATS,THEFIRSTTWOINPUTPARAMETERSMUSTBEVECTORSWITHTHESAMEORIENTATIONINTHESECASESIFTHISISNOTTHECASE,BILINEARDISPLAYSFIRSTTWOARGUMENTSMUSTHAVETHESAMEORIENTATIONMOREABOUTALGORITHMSBILINEARUSESONEOFTWOALGORITHMSDEPENDINGONTHEFORMATOFTHEINPUTLINEARSYSTEMYOUSUPPLYONEALGORITHMWORKSONTHEZEROPOLEGAINFORMATANDTHEOTHERONTHESTATESPACEFORMATFORTRANSFERFUNCTIONREPRESENTATIONS,BILINEARCONVERTSTOSTATESPACEFORM,PERFORMSTHETRANSFORMATION,ANDCONVERTSTHERESULTINGSTATESPACESYSTEMBACKTOTRANSFERFUNCTIONFORMZEROPOLEGAINALGORITHMFORASYSTEMINZEROPOLEGAINFORM,BILINEARPERFORMSFOURSTEPS1IFFPISPRESENT,ITPREWARPSFP2PIFPFSFP/TANFP/FS/2OTHERWISE,FS2FS2ITSTRIPSANYZEROSATUSINGZZFINITEZ3ITTRANSFORMSTHEZEROS,POLES,ANDGAINUSINGPD1P/FS/1P/FSDOBILINEARTRANSFORMATIONZD1Z/FS/1Z/FSKDREALKPRODFSZ/PRODFSP4ITADDSEXTRAZEROSAT1SOTHERESULTINGSYSTEMHASEQUIVALENTNUMERATORANDDENOMINATORORDERSTATESPACEALGORITHMFORASYSTEMINSTATESPACEFORM,BILINEARPERFORMSTWOSTEPS1IFFPISPRESENT,LETIFFPISNOTPRESENT,LETFS2COMPUTEAD,BD,CD,ANDDDINTERMSOFA,B,C,ANDDUSINGREFERENCES1PARKS,TW,ANDCSBURRUSDIGITALFILTERDESIGNNEWYORKJOHNWILEYFREQSB,APLOTFREQUENCYRESPONSELIMITATIONSLOWPASSBESSELFILTERSHAVEAMONOTONICALLYDECREASINGMAGNITUDERESPONSE,ASDOLOWPASSBUTTERWORTHFILTERSCOMPAREDTOTHEBUTTERWORTH,CHEBYSHEV,ANDELLIPTICFILTERS,THEBESSELFILTERHASTHESLOWESTROLLOFFANDREQUIRESTHEHIGHESTORDERTOMEETANATTENUATIONSPECIFICATIONFORHIGHORDERFILTERS,THESTATESPACEFORMISTHEMOSTNUMERICALLYACCURATE,FOLLOWEDBYTHEZEROPOLEGAINFORMTHETRANSFERFUNCTIONCOEFFICIENTFORMISTHELEASTACCURATENUMERICALPROBLEMSCANARISEFORFILTERORDERSASLOWAS15MOREABOUTALGORITHMSBESSELFPERFORMSAFOURSTEPALGORITHM1ITFINDSLOWPASSANALOGPROTOTYPEPOLES,ZEROS,ANDGAINUSINGTHEBESSELAPFUNCTION2ITCONVERTSTHEPOLES,ZEROS,ANDGAININTOSTATESPACEFORM3ITTRANSFORMSTHELOWPASSPROTOTYPEINTOALOWPASSFILTERTHATMEETSTHEDESIGNSPECIFICATIONS4ITCONVERTSTHESTATESPACEFILTERBACKTOTRANSFERFUNCTIONORZEROPOLEGAINFORM,ASREQUIRED14BUTTAPBUTTERWORTHFILTERPROTOTYPESYNTAXZ,P,KBUTTAPNDESCRIPTIONZ,P,KBUTTAPNRETURNSTHEPOLESANDGAINOFANORDERNBUTTERWORTHANALOGLOWPASSFILTERPROTOTYPETHEFUNCTIONRETURNSTHEPOLESINTHELENGTHNCOLUMNVECTORPANDTHEGAININSCALARKZISANEMPTYMATRIXBECAUSETHEREARENOZEROSTHETRANSFERFUNCTIONISBUTTERWORTHFILTERSARECHARACTERIZEDBYAMAGNITUDERESPONSETHATISMAXIMALLYFLATINTHEPASSBANDANDMONOTONICOVERALLINTHELOWPASSCASE,THEFIRST2N1DERIVATIVESOFTHESQUAREDMAGNITUDERESPONSEAREZEROAT0THESQUAREDMAGNITUDERESPONSEFUNCTIONISCORRESPONDINGTOATRANSFERFUNCTIONWITHPOLESEQUALLYSPACEDAROUNDACIRCLEINTHELEFTHALFPLANETHEMAGNITUDERESPONSEATTHECUTOFFANGULARFREQUENCY0ISALWAYSREGARDLESSOFTHEFILTERORDERBUTTAPSETS0TO1FORANORMALIZEDRESULTALGORITHMSZPEXPSQRT1PI122N1/2NPI/2KREALPRODPREFERENCES1PARKS,TW,ANDCSBURRUSDIGITALFILTERDESIGNNEWYORKJOHNWILEYSOS,GZP2SOSZ,P,KCONVERTTOSOSFORMHDDFILTDF2TSOSSOS,GCREATEADFILTOBJECTHFVTOOLHDPLOTMAGNITUDERESPONSESETH,ANALYSIS,FREQDISPLAYFREQUENCYRESPONSELIMITATIONSINGENERAL,YOUSHOULDUSETHEZ,P,KSYNTAXTODESIGNIIRFILTERSTOANALYZEORIMPLEMENTYOURFILTER,YOUCANTHENUSETHEZ,P,KOUTPUTWITHZP2SOSANDANSOSDFILTSTRUCTUREFORHIGHERORDERFILTERSPOSSIBLYSTARTINGASLOWASORDER8,NUMERICALPROBLEMSDUETOROUNDOFFERRORSMAYOCCURWHENFORMINGTHETRANSFERFUNCTIONUSINGTHEB,ASYNTAXTHEFOLLOWINGEXAMPLEILLUSTRATESTHISLIMITATIONN6WN25E629E6/500E6FTYPEBANDPASSTRANSFERFUNCTIONDESIGNB,ABUTTERN,WN,FTYPEH1DFILTDF2B,ATHISISANUNSTABLEFILTERZEROPOLEGAINDESIGNZ,P,KBUTTERN,WN,FTYPESOS,GZP2SOSZ,P,KH2DFILTDF2SOSSOS,GPLOTANDCOMPARETHERESULTSHFVTFVTOOLH1,H2,FREQUENCYSCALE,LOGLEGENDHFVT,TFDESIGN,ZPKDESIGNALGORITHMSBUTTERUSESAFIVESTEPALGORITHM1ITFINDSTHELOWPASSANALOGPROTOTYPEPOLES,ZEROS,ANDGAINUSINGTHEBUTTAPFUNCTION2ITCONVERTSTHEPOLES,ZEROS,ANDGAININTOSTATESPACEFORM3ITTRANSFORMSTHELOWPASSFILTERINTOABANDPASS,HIGHPASS,ORBANDSTOPFILTERWITHDESIREDCUTOFFFREQUENCIES,USINGASTATESPACETRANSFORMATION4FORDIGITALFILTERDESIGN,BUTTERUSESBILINEARTOCONVERTTHEANALOGFILTERINTOADIGITALFILTERTHROUGHABILINEARTRANSFORMATIONWITHFREQU