外文翻译-模拟滤波器

AnalogFiltersBessel,Butterworth,Chebyshev,elliptic,bilineartransformation1Functions1.1bilinear-Bilineartransformationmethodforanalog-to-digitalfilterconversionSyntaxzd,pd,kd=bilinear(z,p,k,fs)zd,pd,kd=bilinear(z,p,k,fs,fp)numd,dend=bilinear(num,den,fs)numd,dend=bilinear(num,den,fs,fp)Ad,Bd,Cd,Dd=bilinear(A,B,C,D,fs)Ad,Bd,Cd,Dd=bilinear(A,B,C,D,fs,fp)DescriptionThebilineartransformationisamathematicalmappingofvariables.Indigitalfiltering,itisastandardmethodofmappingthesoranalogplaneintothezordigitalplane.Ittransformsanalogfilters,designedusingclassicalfilterdesigntechniques,intotheirdiscreteequivalents.Thebilineartransformationmapsthes-planeintothez-planebyThistransformationmapsthejaxis(from=to+)repeatedlyaroundtheunitcircle(ej,from=to)bybilinearcanacceptanoptionalparameterFpthatspecifiesprewarping.fp,inhertz,indicatesamatchfrequency,thatis,afrequencyforwhichthefrequencyresponsesbeforeandaftermappingmatchexactly.Inprewarpedmode,thebilineartransformationmapsthes-planeintothez-planewithWiththeprewarpingoption,bilinearmapsthejaxis(from=to+)repeatedlyaroundtheunitcircle(ej,from=to)byInprewarpedmode,bilinearmatchesthefrequency2fp(inradianspersecond)inthes-planetothenormalizedfrequency2fp/fs(inradianspersecond)inthez-plane.Thebilinearfunctionworkswiththreedifferentlinearsystemrepresentations:zero-pole-gain,transferfunction,andstate-spaceform.Zero-Pole-Gainzd,pd,kd=bilinear(z,p,k,fs)andzd,pd,kd=bilinear(z,p,k,fs,fp)convertthes-domaintransferfunctionspecifiedbyz,p,andktoadiscreteequivalent.Inputszandparecolumnvectorscontainingthezerosandpoles,kisascalargain,andfsisthesamplingfrequencyinhertz.bilinearreturnsthediscreteequivalentincolumnvectorszdandpdandscalarkd.Theoptionalmatchfrequency,fpisinhertzandisusedforprewarping.TransferFunctionnumd,dend=bilinear(num,den,fs)andnumd,dend=bilinear(num,den,fs,fp)convertans-domaintransferfunctiongivenbynumanddentoadiscreteequivalent.Rowvectorsnumanddenspecifythecoefficientsofthenumeratoranddenominator,respectively,indescendingpowersofs.LetB(s)bethenumeratorpolynomialandA(s)bethedenominatorpolynomial.Thetransferfunctionis:fsisthesamplingfrequencyinhertz.bilinearreturnsthediscreteequivalentinrowvectorsnumdanddendindescendingpowersofz(ascendingpowersofz1).fpistheoptionalmatchfrequency,inhertz,forprewarping.State-SpaceAd,Bd,Cd,Dd=bilinear(A,B,C,D,fs)andAd,Bd,Cd,Dd=bilinear(A,B,C,D,fs,fp)convertthecontinuous-timestate-spacesysteminmatricesA,B,C,Dtothediscrete-timesystem:fsisthesamplingfrequencyinhertz.bilinearreturnsthediscreteequivalentinmatricesAd,Bd,Cd,Dd.Theoptionalmatchfrequency,fpisinhertzandisusedforprewarping.Diagnosticsbilinearrequiresthatthenumeratororderbenogreaterthanthedenominatororder.Ifthisisnotthecase,bilineardisplaysNumeratorcannotbehigherorderthandenominator.Forbilineartodistinguishbetweenthezero-pole-gainandtransferfunctionlinearsystemformats,thefirsttwoinputparametersmustbevectorswiththesameorientationinthesecases.Ifthisisnotthecase,bilineardisplaysFirsttwoargumentsmusthavethesameorientation.MoreAboutAlgorithmsbilinearusesoneoftwoalgorithmsdependingontheformatoftheinputlinearsystemyousupply.Onealgorithmworksonthezero-pole-gainformatandtheotheronthestate-spaceformat.Fortransferfunctionrepresentations,bilinearconvertstostate-spaceform,performsthetransformation,andconvertstheresultingstate-spacesystembacktotransferfunctionform.Zero-Pole-GainAlgorithmForasysteminzero-pole-gainform,bilinearperformsfoursteps:1.Iffpispresent,itprewarps:fp=2*pi*fp;fs=fp/tan(fp/fs/2)otherwise,fs=2*fs.2.Itstripsanyzerosatusingz=z(finite(z);3.Ittransformsthezeros,poles,andgainusingpd=(1+p/fs)./(1-p/fs);%Dobilineartransformationzd=(1+z/fs)./(1-z/fs);kd=real(k*prod(fs-z)./prod(fs-p);4.Itaddsextrazerosat-1sotheresultingsystemhasequivalentnumeratoranddenominatororder.State-SpaceAlgorithmForasysteminstate-spaceform,bilinearperformstwosteps:1.Iffpispresent,letIffpisnotpresent,let=fs.2.ComputeAd,Bd,Cd,andDdintermsofA,B,C,andDusingReferences1Parks,T.W.,andC.S.Burrus.DigitalFilterDesign.NewYork:JohnWiley&Sons,1987.Pgs.209-213.2Oppenheim,A.V.,andR.W.Schafer.Discrete-TimeSignalProcessing.UpperSaddleRiver,NJ:Prentice-Hall,1999,pp.450-454.1.2besselap-BesselanaloglowpassfilterprototypeSyntaxz,p,k=besselap(n)Descriptionz,p,k=besselap(n)returnsthepolesandgainofanordernBesselanaloglowpassfilterprototype.nmustbelessthanorequalto25.Thefunctionreturnsthepolesinthelengthncolumnvectorpandthegaininscalark.zisanemptymatrixbecausetherearenozeros.ThetransferfunctionisbesselapnormalizesthepolesandgainsothatatlowfrequencyandhighfrequencytheBesselprototypeisasymptoticallyequivalenttotheButterworthprototypeofthesameorder1.Themagnitudeofthefilterislessthanattheunitycutofffrequencyc=1.AnalogBesselfiltersarecharacterizedbyagroupdelaythatismaximallyflatatzerofrequencyandalmostconstantthroughoutthepassband.ThegroupdelayatzerofrequencyisMoreAboutAlgorithmsbesselapfindsthefilterrootsfromalookuptableconstructedusingSymbolicMathToolboxsoftware.References1Rabiner,L.R.,andB.Gold.TheoryandApplicationofDigitalSignalProcessing.EnglewoodCliffs,NJ:Prentice-Hall,1975.Pgs.228-230.1.3besself-BesselanalogfilterdesignSyntaxb,a=besself(n,Wo)z,p,k=besself(.)A,B,C,D=besself(.)Descriptionbesselfdesignslowpass,analogBesselfilters,whicharecharacterizedbyalmostconstantgroupdelayacrosstheentirepassband,thuspreservingthewaveshapeoffilteredsignalsinthepassband.besselfdoesnotsupportthedesignofdigitalBesselfilters.b,a=besself(n,Wo)designsanordernlowpassanalogBesselfilter,whereWoisthefrequencyuptowhichthefiltersgroupdelayisapproximatelyconstant.Largervaluesofthefilterorder(n)produceagroupdelaythatbetterapproximatesaconstantuptofrequencyWo.besselfreturnsthefiltercoefficientsinthelengthn+1rowvectorsbanda,withcoefficientsindescendingpowersofs,derivedfromthistransferfunction:z,p,k=besself(.)returnsthezerosandpolesinlengthnor2*ncolumnvectorszandpandthegaininthescalark.A,B,C,D=besself(.)returnsthefilterdesigninstate-spaceform,whereA,B,C,andDareanduistheinput,xisthestatevector,andyistheoutput.ExamplesDesignafifth-orderanaloglowpassBesselfilterwithanapproximateconstantgroupdelayupto10,000rad/sandplotthefrequencyresponseofthefilterusingfreqs:b,a=besself(5,10000);freqs(b,a)%PlotfrequencyresponseLimitationsLowpassBesselfiltershaveamonotonicallydecreasingmagnituderesponse,asdolowpassButterworthfilters.ComparedtotheButterworth,Chebyshev,andellipticfilters,theBesselfilterhastheslowestrolloffandrequiresthehighestordertomeetanattenuationspecification.Forhighorderfilters,thestate-spaceformisthemostnumericallyaccurate,followedbythezero-pole-gainform.Thetransferfunctioncoefficientformistheleastaccurate;numericalproblemscanariseforfilterordersaslowas15.MoreAboutAlgorithmsbesselfperformsafour-stepalgorithm:1.Itfindslowpassanalogprototypepoles,zeros,andgainusingthebesselapfunction.2.Itconvertsthepoles,zeros,andgainintostate-spaceform.3.Ittransformsthelowpassprototypeintoalowpassfilterthatmeetsthedesignspecifications.4.Itconvertsthestate-spacefilterbacktotransferfunctionorzero-pole-gainform,asrequired.1.4buttap-ButterworthfilterprototypeSyntaxz,p,k=buttap(n)Descriptionz,p,k=buttap(n)returnsthepolesandgainofanordernButterworthanaloglowpassfilterprototype.Thefunctionreturnsthepolesinthelengthncolumnvectorpandthegaininscalark.zisanemptymatrixbecausetherearenozeros.ThetransferfunctionisButterworthfiltersarecharacterizedbyamagnituderesponsethatismaximallyflatinthepassbandandmonotonicoverall.Inthelowpasscase,thefirst2n-1derivativesofthesquaredmagnituderesponsearezeroat=0.Thesquaredmagnituderesponsefunctioniscorrespondingtoatransferfunctionwithpolesequallyspacedaroundacircleinthelefthalfplane.Themagnituderesponseatthecutoffangularfrequency0isalwaysregardlessofthefilterorder.buttapsets0to1foranormalizedresult.Algorithmsz=;p=exp(sqrt(-1)*(pi*(1:2:2*n-1)/(2*n)+pi/2).;k=real(prod(-p);References1Parks,T.W.,andC.S.Burrus.DigitalFilterDesign.NewYork:JohnWiley&Sons,1987.Chapter7.1.5butter-ButterworthfilterdesignSyntaxz,p,k=butter(n,Wn)z,p,k=butter(n,Wn,ftype)b,a=butter(n,Wn)b,a=butter(n,Wn,ftype)A,B,C,D=butter(n,Wn)A,B,C,D=butter(n,Wn,ftype)z,p,k=butter(n,Wn,s)z,p,k=butter(n,Wn,ftype,s)b,a=butter(n,Wn,s)b,a=butter(n,Wn,ftype,s)A,B,C,D=butter(n,Wn,s)A,B,C,D=butter(n,Wn,ftype,s)Descriptionbutterdesignslowpass,bandpass,highpass,andbandstopdigitalandanalogButterworthfilters.Butterworthfiltersarecharacterizedbyamagnituderesponsethatismaximallyflatinthepassbandandmonotonicoverall.Butterworthfilterssacrificerolloffsteepnessformonotonicityinthepass-andstopbands.UnlessthesmoothnessoftheButterworthfilterisneeded,anellipticorChebyshevfiltercangenerallyprovidesteeperrolloffcharacteristicswithalowerfilterorder.DigitalDomainz,p,k=butter(n,Wn)designsanordernlowpassdigitalButterworthfilterwithnormalizedcutofffrequencyWn.Itreturnsthezerosandpolesinlengthncolumnvectorszandp,andthegaininthescalark.z,p,k=butter(n,Wn,ftype)designsahighpass,lowpass,orbandstopfilter,wherethestringftypeisoneofthefollowing:highforahighpassdigitalfilterwithnormalizedcutofffrequencyWnlowforalowpassdigitalfilterwithnormalizedcutofffrequencyWnstopforanorder2*nbandstopdigitalfilterifWnisatwo-elementvector,Wn=w1w2.Thestopbandisw1w2.bandpassforanorder2*nbandpassfilterifWnisatwo-elementvector,Wn=w1w2.Thepassbandisw1w2.Specifyingatwo-elementvector,Wn,withoutanexplicitftypedefaultstoabandpassfilter.Cutofffrequencyisthatfrequencywherethemagnituderesponseofthefilteris.Forbutter,thenormalizedcutofffrequencyWnmustbeanumberbetween0and1,where1correspondstotheNyquistfrequency,radianspersample.IfWnisatwo-elementvector,Wn=w1w2,butterreturnsanorder2*ndigitalbandpassfilterwithpassbandw1w2.Withdifferentnumbersofoutputarguments,butterdirectlyobtainsotherrealizationsofthefilter.Toobtainthetransferfunctionform,usetwooutputargumentsasshownbelow.Note:SeeLimitationsbelowforinformationaboutnumericalissuesthataffectformingthetransferfunction.b,a=butter(n,Wn)designsanordernlowpassdigitalButterworthfilterwithnormalizedcutofffrequencyWn.Itreturnsthefiltercoefficientsinlengthn+1rowvectorsbanda,withcoefficientsindescendingpowersofz.b,a=butter(n,Wn,ftype)designsahighpass,lowpass,orbandstopfilter,wherethestringftypeishigh,low,orstop,asdescribedabove.Toobtainstate-spaceform,usefouroutputargumentsasshownbelow:A,B,C,D=butter(n,Wn)orA,B,C,D=butter(n,Wn,ftype)whereA,B,C,andDareanduistheinput,xisthestatevector,andyistheoutput.AnalogDomainz,p,k=butter(n,Wn,s)designsanordernlowpassanalogButterworthfilterwithangularcutofffrequencyWnrad/s.Itreturnsthezerosandpolesinlengthnor2*ncolumnvectorszandpandthegaininthescalark.buttersangularcutofffrequencyWnmustbegreaterthan0rad/s.IfWnisatwo-elementvectorwithw1w2,butter(n,Wn,s)returnsanorder2*nbandpassanalogfilterwithpassbandw1w2.z,p,k=butter(n,Wn,ftype,s)designsahighpass,lowpass,orbandstopfilterusingtheftypevaluesdescribedabove.Withdifferentnumbersofoutputarguments,butterdirectlyobtainsotherrealizationsoftheanalogfilter.Toobtainthetransferfunctionform,usetwooutputargumentsasshownbelow:b,a=butter(n,Wn,s)designsanordernlowpassanalogButterworthfilterwithangularcutofffrequencyWnrad/s.Itreturnsthefiltercoefficientsinthelengthn+1rowvectorsbanda,indescendingpowersofs,derivedfromthistransferfunction:b,a=butter(n,Wn,ftype,s)designsahighpass,lowpass,orbandstopfilterusingtheftypevaluesdescribedabove.Toobtainstate-spaceform,usefouroutputargumentsasshownbelow:A,B,C,D=butter(n,Wn,s)orA,B,C,D=butter(n,Wn,ftype,s)whereA,B,C,andDareanduistheinput,xisthestatevector,andyistheoutput.ExamplesHighpassFilterFordatasampledat1000Hz,designa9th-orderhighpassButterworthfilterwithcutofffrequencyof300Hz,whichcorrespondstoanormalizedvalueof0.6:z,p,k=butter(9,300/500,high);sos,g=zp2sos(z,p,k);%ConverttoSOSformHd=dfilt.df2tsos(sos,g);%Createadfiltobjecth=fvtool(Hd);%Plotmagnituderesponseset(h,Analysis,freq)%DisplayfrequencyresponseLimitationsIngeneral,youshouldusethez,p,ksyntaxtodesignIIRfilters.Toanalyzeorimplementyourfilter,youcanthenusethez,p,koutputwithzp2sosandansosdfiltstructure.Forhigherorderfilters(possiblystartingaslowasorder8),numericalproblemsduetoroundofferrorsmayoccurwhenformingthetransferfunctionusingtheb,asyntax.Thefollowingexampleillustratesthislimitation:n=6;Wn=2.5e629e6/500e6;ftype=bandpass;%TransferFunctiondesignb,a=butter(n,Wn,ftype);h1=dfilt.df2(b,a);%Thisisanunstablefilter.%Zero-Pole-Gaindesignz,p,k=butter(n,Wn,ftype);sos,g=zp2sos(z,p,k);h2=dfilt.df2sos(sos,g);%Plotandcomparetheresultshfvt=fvtool(h1,h2,FrequencyScale,log);legend(hfvt,TFDesign,ZPKDesign)Algorithmsbutterusesafive-stepalgorithm:1.Itfindsthelowpassanalogprototypepoles,zeros,andgainusingthebuttapfunction.2.Itconvertsthepoles,zeros,andgainintostate-spaceform.3.Ittransformsthelowpassfilterintoabandpass,highpass,orbandstopfilterwithdesiredcutofffrequencies,usingastate-spacetransformation.4.Fordigitalfilterdesign,butterusesbilineartoconverttheanalogfilterintoadigitalfilterthroughabilineartransformationwithfrequencyprewarping.CarefulfrequencyadjustmentguaranteesthattheanalogfiltersandthedigitalfilterswillhavethesamefrequencyresponsemagnitudeatWnorw1andw2.5.Itconvertsthestate-spacefilterbacktotransferfunctionorzero-pole-gainform,asrequired.1.6cheb1ap-ChebyshevTypeIanaloglowpassfilterprototype1.7cheb2ap-ChebyshevTypeIIanaloglowpassfilterprototype1.8cheby1-ChebyshevTypeIfilterdesign(passbandripple)1.9cheby2-ChebyshevTypeIIfilterdesign(stopbandripple)1.10ellip-Ellipticfilterdesign1.11ellipap-Ellipticanaloglowpassfilterprototype1.12freqs-Frequencyresponseofanalogfilters1.13lp2bp-Transformlowpassanalogfilterstobandpass1.14lp2bs-Transformlowpassanalogfilterstobandstop1.15lp2hp-Transformlowpassanalogfilterstohighpass1.16lp2lp-Changecutofffrequencyforlowpassanalogfilter模拟滤波器贝塞尔，巴特沃斯，切比雪夫，椭圆形，双线性变换1功能1.1双线性-用于模拟-数字转换滤波器的双线性变换法用法zd,pd,kd=bilinear(z,p,k,fs)zd,pd,kd=bilinear(z,p,k,fs,fp)numd,dend=bilinear(num,den,fs)numd,dend=bilinear(num,den,fs,fp)Ad,Bd,Cd,Dd=bilinear(A,B,C,D,fs)Ad,Bd,Cd,Dd=bilinear(A,B,C,D,fs,fp)说明双线性变换是变量的数学映射。在数字滤波，它是s或模拟平面映射到z或者数字平面的一种标准方法。它把模拟滤波器，采用经典的滤波器设计技术，为他们的离散等价物而设计的。双线性变换由18)(zafsHz映射s平面到z平面。双线性可以接受一个可选的参数，Fp，指定预畸变。fp，单位为赫兹，表示“匹配”的频率，也就是一个频率的之前和之后的映射匹配频率响应完全相同。在prewarped模式，使用1tan28)(zfpsHz双线性变换映射s平面到Z-平面。随着预畸变选项，双线性映射反复围绕单位圆(ejw,从到)由的虚轴(从到+)。pzf2)tan(21在prewarped模式，双线性在s平面的归一化频率2fp/fs（弧度每秒）在z平面上的频率2fp（弧度每秒）相匹配。双线性函数的工作原理有三个不同的线性系统表示：零极点增益，传递函数，状态空间形式。零极点增益ZD，PD，KD=双线性（Z，P，K，FS）和ZD，PD，KD=双线性（Z，P，K，FS，FP）转换为z指定的s域传递函数，p和k以一个离散当量。输入z和p分别含有零点和极点列向量，k是一个标量增益，并且fs是在赫兹的采样频率。双线性返回的列向量ZD和PD和标量KD离散等价的。可选的匹配次数，FP是赫兹和用于预畸变。传递函数numd，DEND=双线性（NUM，书房，FS）和numd，DEND=双线性（NUM，书房，FS，FP）转换由Num和书房的离散相当于给予s域传递函数。行向量Num和书房指定的分子和分母的系数，分别按降序s的能力。设B（s）为分子多项式和A（s）为分母多项式。传递函数是：。)1(.)1(nAABsnFS是赫兹的采样频率。双线性返回离散等效于行向量numd和DEND降序z与权力（升序Z-1的权力）。fp是可选的匹配频率，以赫兹为单位，对预畸变。状态空间AD，BD，CD，DD=双线性（A，B，C，D，FS）和AD，BD，CD，DD=双线性（A，B，C，D，FS，FP）转换为连续-时间状态空间系统在矩阵A，B，C，DDuCxyBA到离散时间系统：1nnxddFS是赫兹的采样频率。双线性返回离散相当于矩阵AD，BD，CD，DD。可选的匹配次数，FP是赫兹和用于预畸变。诊断双线性要求分子阶数不大于分母阶更大。如果不是这种情况，双线性显示分子不能高阶比的分母。对于双线性到零极点增益和传递函数的线性系统格式区分，前两个输入参数必须是具有相同的取向在这些情况下，向量。如果不是这种情况，双线性显示前两个参数必须具有相同的方向。算法根据您提供的输入线性系统的格式双线性使用两种算法之一。一个算法的工作原理上的状态空间形式的零极点增益形式和其他。对于传递函数表示法，双线性转换为状态空间形式，进行了改造，产生的状态空间系统转换回传输函数形式。零极点增益算法对于零极点增益形式的系统，双线性执行四个步骤：1.若fp存在，它具有频率予翘曲的双线性变换(Tustin)法fp=2*pi*fp;fs=fp/tan(fp/fs/2)否则，fs=2*fs.2.它去掉任何零点在采用z=z(finite(z);3.它采用变换的零点，极点和增益PD=（1+P/FS）/（1-p/fs）;做双线性变换ZD=（1+Z/FS）/（1-z/fs）;kd=real(k*prod(fs-z)./prod(fs-p);4.它增加了额外的零在-1使该系统具有等效的分子和分母秩序。状态空间算法对于状态空间形式的系统，双线性执行两个步骤：1.如果FP存在，让)tan(8fp若fp是不存在，取=FS。计算AD，BD，CD和DD在使用A，B，C和D的条款)tan(8fp文献1Parks,ThomasW.,andC.SidneyBurrus.DigitalFilterDesign.NewYork:JohnWiley&Sons,1987,pp.209213.2Oppenheim,AlanV.,RonaldW.Schafer,andJohnR.Buck.Discrete-TimeSignalProcessing.UpperSaddleRiver,NJ:PrenticeHall,1999,pp.450454.1.2besselap贝塞尔模拟低通滤波器原型句法z,p,k=besselap(n)描述Z，P，K=besselap（n）返回两极的N阶贝塞尔模拟低通滤波器原型和增益。n必须小于或等于25。该函数返回的极点在长度为n的列向量p和标量k中的增益。z是一个空矩阵，因为没有零。传递函数是besselap标准化的极点和增益，以使在)().2(1()npspsksH低频率和高频率的贝塞尔原型是渐近相当于巴特沃思原型的顺序相同的1。过滤器的幅度小于在统一的截止频率为c=1。模拟贝塞尔滤波器的特征是一组延迟是最平坦的频率为零时，几乎恒定的整个通带。群延迟在零频率n1!2)(更多算法besselap发现过滤器的根从查找表使用符号数学工具箱软件构建。1.3besself贝塞尔模拟滤波器设计句法b,a=besself(n,Wo)z,p,k=besself(.)A,B,C,D=besself(.)描述besself设计低通，模拟贝塞尔滤波器，其特点是在整个通带内几乎恒定的群延迟，从而保持滤波的信号的波形通带。besself不支持的数字贝塞尔滤波器的设计。B，A=besself（正，禾）设计了一个n阶低通模拟贝塞尔滤波器，其中禾是主频高达该滤波器的群时延近似为常数。滤波器阶数（n）的值越大，产生群时延能够更加接近于一个常数高达频率窝。besself返回的长度n+1个行向量b和a的滤波器系数，与降序第权力，从这个传递函数的系数得出：)1(.)1()(nassbABsHnZ，P，K=besself（.）返回零点和极点的长度为n或2*N的列向量z和p和在标量k中的增益。A，B，C，D=besself（.）返回的滤波器设计的状态空间形式，其中A，B，C和D是公式和u为输入，x是状态矢量，而y是输出。举例一个模拟贝塞尔FilterDesign五阶模拟低通贝塞尔滤波器大约恒定的群延迟至10,000弧度/秒的频率响应。使用FREQS画出滤波器的幅度和相位响应。b,a=besself(5,10000);freqs(b,a)限制低通贝塞尔滤波器有一个单调递减的幅度响应，因为做低通Butterworth滤波器。相较于巴特沃斯，切比雪夫和椭圆滤波器，贝塞尔滤波器具有最慢的衰减和需要最高为满足衰减规范。对于高阶滤波器的状态空间形式是最准确的数字，后跟零极点增益形式。传递函数系数的形式是最不准确的，可能会出现过滤器订单低至15数值问题。更多Algorithmsbesself进行四步算法：1.It发现低通模拟原型的极点，零点和增益使用besselap功能。2.2的极点，零点和增益转换成状态空间形式。3.It变换低通原型到符合设计规范的低通滤波器。4.4根据需要转换的状态空间滤波反传递函数或零极点增益形式。1.4buttap巴特沃斯滤波器原型句法z,p,k=buttap(n)Z，P，K=buttap（n）返回的极点的n阶巴特沃斯模拟低通滤波器原型和增益。该函数返回的极点在长度为n的列向量p和标量k中的增益。z是一个空矩阵，因为没有零。传递函数是)().2(1()(npspsszH巴特沃斯滤波器的特征是幅度响应是在通带和单调的整体最平坦的。在该低通的情况下，平方幅度响应的第2n-1个导数为零，在=0。的平方幅度响应函数是nH202)(1)对应于与磁极周围的圆等距分布在左半平面的传递函数。在截止角频率0的幅度响应总是不管滤波器的阶数。buttap套0为1的归一化结果算法z=;p=exp(sqrt(-1)*(pi*(1:2:2*n-1)/(2*n)+pi/2).;k=real(prod(-p);参考文献1Parks,T.W.,andC.S.Burrus.DigitalFilterDesign.NewYork:JohnWiley&Sons,1987.Chapter7.1.5butter巴特沃斯滤波器的设计句法z,p,k=butter(n,Wn)z,p,k=butter(n,Wn,ftype)b,a=butter(n,Wn)b,a=butter(n,Wn,ftype)A,B,C,D=butter(n,Wn)A,B,C,D=butter(n,Wn,ftype)z,p,k=butter(n,Wn,s)z,p,k=butter(n,Wn,ftype,s)b,a=butter(n,Wn,s)b,a=butter(n,Wn,ftype,s)A,B,C,D=butter(n,Wn,s)A,B,C,