通信与电子信息专业英语 课件 Unit 5 Digital Signal Processing

Unit5DigitalSignalProcessing5.1IntroductiontoDigitalSignalProcessing

5.2StructuresforDiscrete-TimeSystem

5.3FilterDesignTechniques5.1IntroductiontoDigitalSignalProcessingWordsandExpressionsBackgroundsTextWordsandExpressionsMoore’sLaw 摩尔定律GordonEarleMoore(January3,1929–March24,2023)wasanAmericanbusinessman,engineer,andthe

co-founder

andemerituschairmanof

IntelCorporation.Heproposed

Moore'slaw

whichmakestheobservationthatthe

numberoftransistors

inan

integratedcircuit

(IC)doublesabouteverytwoyears.WordsandExpressions5Moore’sLaw–NowandintheFutureMoore’sLawhasalwaysbeenaboutinnovationandwecanconfidentlysayinnovationcontinuesunabated.By

Dr.AnnKelleherExecutiveVicePresidentGeneralManagerofTechnologyDevelopmentWordsandExpressions6microprocessor n.微处理器transformation n.变换FourierTransformLaplaceTransformZTransformAmodern

64bit

x86-64

processor(AMDRyzen52600,Basedon

Zen+,2017)WordsandExpressionsconvolution n.卷积parameter n.参数preprocessing n.预处理7Discrete2DConvolutionAnimationconvolutionkernelWordsandExpressionsmodulation n.调制8CategorizationforsignalmodulationbasedondataandcarriertypesAlow-frequencymessagesignal(top)maybecarriedbyanAMorFMradiowave.WordsandExpressions9signalconditioning信号调理Signalconditioningisanelectroniccircuitthatmanipulatesasignalinawaythatpreparesitforthenextstageofprocessing.Signalconditionerisoneofthefundamentalbuildingblocksofmoderndataacquisition(akaDASorDAQsystem).compression n.压缩compressionstandards:JPEG\MPEG\H.264WordsandExpressions10transmission n.传输communicationchannel通信信道A

communicationchannel

referseithertoaphysical

transmissionmedium

suchasawire,ortoa

logicalconnection

overa

multiplexed

mediumsuchasaradiochannelin

telecommunications

and

computernetworking.A

TOSLINK

opticalfibercablewithaclearjacket.Thesecablesareusedmainlyfordigitalaudioconnectionsbetweendevices.WordsandExpressions11postprocessing n.后处理receiver n.接收机facsimile n.传真；复制本analog adj.模拟的chip n.芯片WordsandExpressionsanalogtodigital(A/D)conversion 模数转换digitaltoanalog(D/A)conversion 数模转换12An8-levelADCcodingscheme8-channel

CirrusLogic

CS4382digital-to-analogconverterasusedina

soundcard.WordsandExpressionsfastFouriertransform(FFT)algorithm 快速傅里叶变换multiratetechnique 多采样率技术polyphasefilterimplementation 多相位滤波器实现13AnexampleFFTalgorithmstructure,usingadecompositionintohalf-sizeFFTsIn

digitalsignalprocessing,

upsampling,

expansion,and

interpolation（内插）

aretermsassociatedwiththeprocessof

resampling

ina

multiratedigitalsignalprocessing

system.Downsampling,

compression,and

decimation（抽取）

aretermsassociatedwiththeprocessof

resampling

ina

multi-ratedigitalsignalprocessing

system.

WordsandExpressionswavelet n.小波expansion n.展开sequence n.序列14MorletandMexicanhatAnexampleofthe2D

discretewavelettransform

thatisusedin

JPEG2000.WordsandExpressionsquantization n.量化biomedicalengineering生物医学工程Biomedicalengineering

(BME)or

medicalengineering

istheapplicationofengineeringprinciplesanddesignconceptstomedicineandbiologyforhealthcarepurposes(e.g.,diagnosticortherapeutic).153-bitresolutionwitheightlevels.WordsandExpressionsone-dimensional adj.一维的multidimensional adj.多维的16A2-Dfilter(left)definedbyits1-Dprototypefunction(right)andaMcClellantransformation.WordsandExpressions17telecommunication n.电信microelectronictechnology微电子技术asubfieldofelectronicthestudyandmanufactureofverysmallelectronicdesignsandcomponentsBackgrounds18DigitalSignalProcessing/courses/res-6-008-digital-signal-processing-spring-2011/TextOutlineBasicsofSignalProcessingDiscrete-timeSignalProcessingMultidimensionalSignalProcessingDevelopmentsofSignalProcessing19BasicsofSignalProcessingSignalprocessingapplicationsspananimmensesetofdisciplinesthatincludeentertainment,communications,spaceexploration,medicine,archeology,geophysics,justtonameafew.信号处理应用涵盖了一系列学科，包括娱乐、通信、太空探索、医学、考古学、地球物理学等等。20BasicsofSignalProcessingBysomeestimates,evenwithimpendinglimitationsonMoore’sLaw,theprocessingcapabilityofbothspecial-purposesignalprocessingmicroprocessorsandpersonalcomputersislikelytoincreasebyseveralordersofmagnitude.据估计，即使摩尔定律即将受到限制，专用信号处理微处理器和个人计算机的处理能力也可能增加几个数量级。21BasicsofSignalProcessingSignalprocessingdealswiththerepresentation,transformation,andmanipulationofsignalsandtheinformationthesignalscontain.信号处理关注的是信号及其所包含信息的表示、变换和处理。22BasicsofSignalProcessingIncommunicationsystem,itisgenerallynecessarytodopreprocessingsuchasmodulation,signalconditioning,andcompressionpriortotransmissionoveracommunicationschannel,andthentocarryoutpostprocessingatthereceivertorecoverafacsimileoftheoriginalsignal.在通信系统中，信号在一条信道上传输之前一般要做一些像调制、信号调理和压缩等这样的预处理，然后在接收机处进行后处理以恢复原始信号。23BasicsofSignalProcessingThesedevelopmentsintechnologyhavebeenreinforcedbymanyimportanttheoreticaldevelopments,suchasthefastFouriertransform(FFT)algorithm,parametricsignalmodeling,multiratetechniques,polyphasefilterimplementation,andnewwaysofrepresentingsignals,suchaswaveletexpansions.许多重要的理论发展加强了技术的发展，如快速傅立叶变换（FFT）算法、参数信号建模、多速率技术、多相滤波器实现，以及表示信号的新方法，如小波展开。24Discrete-timeSignalProcessingDiscrete-timesignalprocessingisbasedonprocessingofnumericsequencesindexedonintegervariablesratherthanfunctionsofacontinuousindependentvariable.离散时间信号处理是基于对以整数变量为索引的数字序列的处理，而不是连续自变量的函数。25Discrete-timeSignalProcessingAscomputerspeedshaveincreased,discrete-timeprocessingofcontinuous-timesignalsinrealtimehasbecomecommonplaceincommunicationsystems,radarandsonar,speechandvideocodingandenhancement,biomedicalengineering,andmanyotherareasofapplications.随着计算机速度的提高，在通信系统、雷达和声纳、语音和视频编码与增强、生物医学工程及许多其他应用领域，对连续时间信号进行实时离散时间处理已变得司空见惯。26MultidimensionalSignalProcessingManyimageprocessingapplicationsrequiretheuseoftwo-dimensionalsignalprocessingtechniques.Thisisthecaseinsuchareasasvideocoding,medicalimaging,enhancementandanalysisofaerialphotographs,analysisofsatelliteweatherphotos,andenhancementofvideotransmissionsfromlunaranddeep-spaceprobes.许多图像处理应用需要使用二维信号处理技术。视频编码、医学成像、航空图像的增强和分析、卫星天气图像的分析以及月球和深空探测器视频传输的增强等领域都是如此。27DevelopmentsofSignalProcessingAnotableexampleisintheareaoftelecommunications,wherediscrete-timesignalprocessingtechniques,microelectronictechnology,andfiberoptictransmissionhavecombinedtochangethenatureofcommunicationsystemsintrulyrevolutionaryways.电信领域就是一个明显的例子，在该领域中，离散时间信号处理技术、微电子技术和光纤传输技术的结合，正以真正革命性的方式改变着通信系统的面貌。285.2StructuresforDiscrete-TimeSystemWordsandExpressionsBackgroundsTextWordsandExpressions30rational adj.有理的(eg.rationalfraction)Arationalfunctionisafunctionthatcanbewrittenasaquotientoftwopolynomialfunctions.Insymbols,thefunction: iscalledarationalfunction.systemfunction 系统函数transferfunction 传递函数WordsandExpressionsinterconnection n.互连constant n.常数delay n.延迟InterconnectionofLTIsystemsWordsandExpressionsformula n.公式expression 表达式equation 等式inequality 不等式LinearconstantcoefficientdifferenceequationWordsandExpressionsrecursive adj.递归的Incomputerprogramming,thetermrecursivedescribesafunctionormethodthatrepeatedlycalculatesasmallerpartofitselftoarriveatthefinalresult.Itissimilartoiteration,butinsteadofrepeatingasetofoperations,arecursivefunctionaccomplishesrepetitionbyreferringtoitselfinitsowndefinition.WordsandExpressionsinitial-restcondition 初始松弛条件Thedefinitionofinitialrestconditionforasystemingeneralisthatifx(t)=0fort<t0theny(t)=0fort<t0.

Fordiscretetimesystems,itbasicallysaysthat

theinputiszerouptoacertainpoint(orx[n]=0forn<n0),thentheoutputshouldbezerouptothesamepoint(ory[n]=0forn<n0).recurrence n.重现WordsandExpressionsblockdiagram 方框图cascade n.级联canonicformimplementation 规范形式实现Cascadestructurefora6th–ordersystemwithadirectformIIrealizationofeach2nd-ordersubsystemCanonicformimplementationofNth–orderLTIsystemBackgrounds36UCBerkeleyEE123.DigitalSignalProcessing/Courses/EE123/TextOutline37Representationsfordiscrete-timesystemDifferenceEquationImplementationBasicElementsBlockDiagramsRepresentationsfordiscrete-timesystemAnLTIsystemwitharationalsystemfunctionhasthepropertythattheinputandoutputsequencessatisfyalinearconstant-coefficientdifferenceequation.具有有理系统函数的线性时不变系统有这样的性质，即其输入和输出序列满足线性常系数差分方程。38

39Representationsfordiscrete-timesystemSystemsdescribedbylinearconstant-coefficientdifferenceequationscanberepresentedbystructuresconsistingofaninterconnectionofthebasicoperationsofaddition,multiplicationbyaconstant,anddelay,theexactimplementationofwhichisdictatedbythetechnologytobeused.由线性常系数差分方程描述的系统能够用由加法、常数乘法和延迟的基本运算互连而成的结构来表示，它的真正实现则取决于所用的技术。40Representationsfordiscrete-timesystemBasicElementsThebasicelementsrequiredfortheimplementationofanLTIdiscrete-timesystemsareadders,multipliers,andmemoryforstoringdelayedsequencevaluesandcoefficients.实现线性时不变离散时间系统所需的基本单元是加法器、乘法器和存储延迟序列值和系数的存贮器。41BasicElements42Figure5.1Blockdiagramsymbols.Additionoftwosequences.Multiplicationofasequencebyaconstant.Unitdelay.BlockDiagram43

Ablockdiagramcanberearrangedormodifiedinavarietyofwayswithoutchangingtheoverallsystemfunction.Eachappropriaterearrangementrepresentsadifferentcomputationalalgorithmforimplementingthesamesystem.在不改变整个系统函数的情况下，可以各种方式重新排列或修改框图。每个适当的重排表示用于实现相同系统的不同计算算法。44BlockDiagramSinceeachofthetwosystemsisanLTIsystem(assuminginitial-restconditionsforthedelayregisters),theorderinwhichthetwosystemsarecascadedcanbereversed,asshowninFigure5.3,withoutaffectingtheoverallsystemfunction.由于两个系统都是线性时不变系统（假设延迟寄存器初始松弛），那么两个系统在级联中的次序就可以交换成如图5.3所示，而不会影响总的系统函数。45BlockDiagram46Figure5.3Rearrangementofblockdiagramofmiddlefigure.BlockDiagramConsequently,thetwocanbecollapsedintoonechain,asindicatedinFigure5.4.Animplementationwiththeminimumnumberofdelayelementsiscommonlyreferredtoasacanonicformimplementation.因此，如图5.4所示，两者可以折叠成一条链。具有最小数量延迟单元的实现通常被称为规范形式实现。47BlockDiagramBlockDiagram48Figure5.4ThedirectformIIorcanonicdirectformimplementation.5.3FilterDesignTechniquesWordsandExpressionsBackgroundsTextWordsandExpressionsbilineartransformation 双线性变换法Thebilineartransformisaspecialcaseofaconformalmapping,oftenusedtoconvertatransferfunction

Ha(s)ofalinear,time-invariant(LTI)filterinthecontinuous-timedomain(oftencalledananalogfilter)toatransferfunctionHd(z)ofalinear,shift-invariantfilterinthediscrete-timedomain.

51WordsandExpressionsaliasing n.混叠WordsandExpressionspassband n.通带stopband n.阻带transition n.过渡带tolerance n.容限causal adj.因果的Lowpassfiltertolerancescheme.Inordertobeimplementable,anytime-dependentfilter(operatinginrealtime)mustbe

causal:thefilterresponseonlydependsonthecurrentandpastinputs.Backgrounds53CMUDigitalSignalProcessing/~ee791/TextOutline54TypesofDigitalFiltersInfiniteImpulseResponse(IIR)filterFiniteImpulseResponse(FIR)filterFilterDesignTechniquesIIR:impulseinvariance,bilineartransformationFIR:windowfunction,optimumapproximationEconomicConcernsTypesofDigitalFiltersFiltersareaparticularlyimportantclassofLTIsystems.Strictlyspeaking,thetermfrequency-selectivefiltersuggestsasystemthatpassescertainfrequencycomponentsofaninputsignalandtotallyrejectsallothers,butinabroadercontext,anysystemthatmodifiescertainfrequenciesrelativetoothersisallcalledfilter.滤波器是LTI系统中一类特别重要的系统。严格来说，选频滤波器指的是让输入信号的某些频率分量通过并完全抑制所有其他频率分量的系统，但在更广泛的定义下，任何相对于其他频率分量修改特定频率分量的系统都被称为滤波器。55TypesofDigitalFiltersThedesignofdiscrete-timefilterscorrespondstodeterminingtheparametersofatransferfunctionordifferenceequationthatapproximatesadesiredimpulseresponseorfrequencyresponsewithinspecifiedtolerances.离散时间滤波器的设计即确定其传递函数或差分方程的参数，由此得到近似于规定容限内的期望系统的脉冲响应或频率响应。56TypesofDigitalFiltersDiscrete-timesystemsimplementedwithdifferenceequationsfallintotwobasiccategories:infiniteimpulseresponse(IIR)systemsandfiniteimpulseresponse(FIR)systems.用差分方程实现的离散时间系统分为两类：无限脉冲响应（IIR，也译为无限冲激响应）系统和有限脉冲响应（FIR，也译为有限冲激响应）系统。57TypesofDigitalFiltersDesigningIIRfiltersimpliesobtaininganapproximatingtransferfunctionthatisrationalfunctionofz,whereasdesigningFIRfiltersimpliespolynomialapproximation.设计IIR滤波器意味着获得近似的传递函数，该传递函数是z变量的有理函数，而设计FIR滤波器则意味着多项式逼近。58FilterdesigntechniquesWhendiscrete-timefiltersfirstcameintocommonuse,theirdesignwerebasedonmappingwell-formulatedandwell-understoodcontinuous-timefilterdesignstodiscrete-timedesignsthroughtechniquessuchasimpulseinvarianceandthebilineartransformation.当离散时间滤波器首次普遍使用时，它们的设计是通过脉冲（冲激）响应不变法和双线性变换法等技术将精心设计且易于理解的连续时间滤波器设计映射到离散时间滤波器的设计。59FilterdesigntechniquesTheuseofthisproceduremaybemotivatedbyadesiretomaintaintheshapeoftheimpulseresponseorbytheknowledgethatifthecontinuous-timefilterisbandlimited,consequentlythediscrete-timefilterfrequencyresponsewillcloselyapproximatethecontinuous-timefrequencyresponse.使用本方法的出发点可能是希望保持冲激响应的形状，或者若已知连续时间滤波器是带限的，那么离散时间滤波器的频率响应将非常接近连续时间滤波器的频率响应。60Filterdesigntechniques

61FilterdesigntechniquesThedesignoffiltersinvolvesthefollowingstages,thespecificationofthedesiredpropertiesofthesystem,theapproximationofthespecificationsusingacausaldiscrete-timesystem,andtherealizationofthesystem.滤波器的设计涉及以下步骤：给定系统所要求特性的技术指标、用因果离散时间系统逼近这些技术指标及实现该系统。62Filterdesigntechniques63Figure5.5Lowpassfiltertolerancescheme.FilterdesigntechniquesManyofthefiltersusinginpracticearespecifiedbyatoleranceschemewithnoconstraintsonthephaseresponse

otherthanthoseimposedimplicitlybyrequirementsofstabilityandcausality.在实践中使用的许多滤波器是由容限方案指定的，除了稳定性和因果关系要求隐含施加的约束之外，对相位响应没有任何约束。64FilterdesigntechniquesForthedesignofFIRfilters,windowfunctionmethodandoptimumapproximationmethodareapplied.ThechoicebetweenanFIRfilterandanIIRfilterdependsontheimportancetothedesignproblemoftheadvantagesofeachtype.IIRfilters,forexample,havetheadvantagethatavarietyoffrequency-selectivefilterscanbedesignedusingclosed-formdesignformulas.FIR滤波器的设计采用了窗函数法和最优逼近法。FIR滤波器和IIR滤波器之间的选择取决于每种类型的优点对设计问题的重要性。例如，IIR滤波器的优点是，可以使用闭合形式的设计公式来设计各种频率选择性滤波器。65FilterdesigntechniquesAlthoughthewindowmethodisstraightforwardtoapply,someiterationmaybenecessarytomeetaprescribedspecification.TheParks-McClellanalgorithmleadstolowerorderfiltersthanthewindowmethoddoes,andbothmethodscanbeimplementedonapersonalcomputeroraworkstation.尽管窗函数法应用起来很简单，但为满足规定的技术指标，可能需要进行一些迭代。Parks-McClellan算法比窗函数法设计的滤波器阶次低，并且这两种方法都可以在个人计算机或工作站上实现。66EconomicConcernsClearly,thefinalchoicewillmostoftenbemadebyengineeringjudgementonsuchquestionsastheformulationofthespecifications,themethodofimplementationofthefilter,andthecomputationalfacilitiesandsof