通信與電子信息專業(yè)英語 課件 Unit 5 Digital Signal Processing

Unit5DigitalSignalProcessing5.1IntroductiontoDigitalSignalProcessing

5.2StructuresforDiscrete-TimeSystem

5.3FilterDesignTechniques5.1IntroductiontoDigitalSignalProcessingWordsandExpressionsBackgroundsTextWordsandExpressionsMoore’sLaw 摩爾定律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.微處理器transformation n.變換FourierTransformLaplaceTransformZTransformAmodern

64bit

x86-64

processor(AMDRyzen52600,Basedon

Zen+,2017)WordsandExpressionsconvolution n.卷積parameter n.參數(shù)preprocessing n.預(yù)處理7Discrete2DConvolutionAnimationconvolutionkernelWordsandExpressionsmodulation n.調(diào)制8CategorizationforsignalmodulationbasedondataandcarriertypesAlow-frequencymessagesignal(top)maybecarriedbyanAMorFMradiowave.WordsandExpressions9signalconditioning信號調(diào)理Signalconditioningisanelectroniccircuitthatmanipulatesasignalinawaythatpreparesitforthenextstageofprocessing.Signalconditionerisoneofthefundamentalbuildingblocksofmoderndataacquisition(akaDASorDAQsystem).compression n.壓縮compressionstandards:JPEG\MPEG\H.264WordsandExpressions10transmission n.傳輸communicationchannel通信信道A

communicationchannel

referseithertoaphysical

transmissionmedium

suchasawire,ortoa

logicalconnection

overa

multiplexed

mediumsuchasaradiochannelin

telecommunications

and

computernetworking.A

TOSLINK

opticalfibercablewithaclearjacket.Thesecablesareusedmainlyfordigitalaudioconnectionsbetweendevices.WordsandExpressions11postprocessing n.后處理receiver n.接收機facsimile n.傳真；復(fù)制本analog adj.模擬的chip n.芯片WordsandExpressionsanalogtodigital(A/D)conversion 模數(shù)轉(zhuǎn)換digitaltoanalog(D/A)conversion 數(shù)模轉(zhuǎn)換12An8-levelADCcodingscheme8-channel

CirrusLogic

CS4382digital-to-analogconverterasusedina

soundcard.WordsandExpressionsfastFouriertransform(FFT)algorithm 快速傅里葉變換multiratetechnique 多采樣率技術(shù)polyphasefilterimplementation 多相位濾波器實現(xiàn)13AnexampleFFTalgorithmstructure,usingadecompositionintohalf-sizeFFTsIn

digitalsignalprocessing,

upsampling,

expansion,and

interpolation（內(nèi)插）

aretermsassociatedwiththeprocessof

resampling

ina

multiratedigitalsignalprocessing

system.Downsampling,

compression,and

decimation（抽取）

aretermsassociatedwiththeprocessof

resampling

ina

multi-ratedigitalsignalprocessing

system.

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

discretewavelettransform

thatisusedin

JPEG2000.WordsandExpressionsquantization n.量化biomedicalengineering生物醫(yī)學(xué)工程Biomedicalengineering

(BME)or

medicalengineering

istheapplicationofengineeringprinciplesanddesignconceptstomedicineandbiologyforhealthcarepurposes(e.g.,diagnosticortherapeutic).153-bitresolutionwitheightlevels.WordsandExpressionsone-dimensional adj.一維的multidimensional adj.多維的16A2-Dfilter(left)definedbyits1-Dprototypefunction(right)andaMcClellantransformation.WordsandExpressions17telecommunication n.電信microelectronictechnology微電子技術(shù)asubfieldofelectronicthestudyandmanufactureofverysmallelectronicdesignsandcomponentsBackgrounds18DigitalSignalProcessing/courses/res-6-008-digital-signal-processing-spring-2011/TextOutlineBasicsofSignalProcessingDiscrete-timeSignalProcessingMultidimensionalSignalProcessingDevelopmentsofSignalProcessing19BasicsofSignalProcessingSignalprocessingapplicationsspananimmensesetofdisciplinesthatincludeentertainment,communications,spaceexploration,medicine,archeology,geophysics,justtonameafew.信號處理應(yīng)用涵蓋了一系列學(xué)科，包括娛樂、通信、太空探索、醫(yī)學(xué)、考古學(xué)、地球物理學(xué)等等。20BasicsofSignalProcessingBysomeestimates,evenwithimpendinglimitationsonMoore’sLaw,theprocessingcapabilityofbothspecial-purposesignalprocessingmicroprocessorsandpersonalcomputersislikelytoincreasebyseveralordersofmagnitude.據(jù)估計，即使摩爾定律即將受到限制，專用信號處理微處理器和個人計算機的處理能力也可能增加幾個數(shù)量級。21BasicsofSignalProcessingSignalprocessingdealswiththerepresentation,transformation,andmanipulationofsignalsandtheinformationthesignalscontain.信號處理關(guān)注的是信號及其所包含信息的表示、變換和處理。22BasicsofSignalProcessingIncommunicationsystem,itisgenerallynecessarytodopreprocessingsuchasmodulation,signalconditioning,andcompressionpriortotransmissionoveracommunicationschannel,andthentocarryoutpostprocessingatthereceivertorecoverafacsimileoftheoriginalsignal.在通信系統(tǒng)中，信號在一條信道上傳輸之前一般要做一些像調(diào)制、信號調(diào)理和壓縮等這樣的預(yù)處理，然后在接收機處進行后處理以恢復(fù)原始信號。23BasicsofSignalProcessingThesedevelopmentsintechnologyhavebeenreinforcedbymanyimportanttheoreticaldevelopments,suchasthefastFouriertransform(FFT)algorithm,parametricsignalmodeling,multiratetechniques,polyphasefilterimplementation,andnewwaysofrepresentingsignals,suchaswaveletexpansions.許多重要的理論發(fā)展加強了技術(shù)的發(fā)展，如快速傅立葉變換（FFT）算法、參數(shù)信號建模、多速率技術(shù)、多相濾波器實現(xiàn)，以及表示信號的新方法，如小波展開。24Discrete-timeSignalProcessingDiscrete-timesignalprocessingisbasedonprocessingofnumericsequencesindexedonintegervariablesratherthanfunctionsofacontinuousindependentvariable.離散時間信號處理是基于對以整數(shù)變量為索引的數(shù)字序列的處理，而不是連續(xù)自變量的函數(shù)。25Discrete-timeSignalProcessingAscomputerspeedshaveincreased,discrete-timeprocessingofcontinuous-timesignalsinrealtimehasbecomecommonplaceincommunicationsystems,radarandsonar,speechandvideocodingandenhancement,biomedicalengineering,andmanyotherareasofapplications.隨著計算機速度的提高，在通信系統(tǒng)、雷達和聲納、語音和視頻編碼與增強、生物醫(yī)學(xué)工程及許多其他應(yīng)用領(lǐng)域，對連續(xù)時間信號進行實時離散時間處理已變得司空見慣。26MultidimensionalSignalProcessingManyimageprocessingapplicationsrequiretheuseoftwo-dimensionalsignalprocessingtechniques.Thisisthecaseinsuchareasasvideocoding,medicalimaging,enhancementandanalysisofaerialphotographs,analysisofsatelliteweatherphotos,andenhancementofvideotransmissionsfromlunaranddeep-spaceprobes.許多圖像處理應(yīng)用需要使用二維信號處理技術(shù)。視頻編碼、醫(yī)學(xué)成像、航空圖像的增強和分析、衛(wèi)星天氣圖像的分析以及月球和深空探測器視頻傳輸?shù)脑鰪姷阮I(lǐng)域都是如此。27DevelopmentsofSignalProcessingAnotableexampleisintheareaoftelecommunications,wherediscrete-timesignalprocessingtechniques,microelectronictechnology,andfiberoptictransmissionhavecombinedtochangethenatureofcommunicationsystemsintrulyrevolutionaryways.電信領(lǐng)域就是一個明顯的例子，在該領(lǐng)域中，離散時間信號處理技術(shù)、微電子技術(shù)和光纖傳輸技術(shù)的結(jié)合，正以真正革命性的方式改變著通信系統(tǒng)的面貌。285.2StructuresforDiscrete-TimeSystemWordsandExpressionsBackgroundsTextWordsandExpressions30rational adj.有理的(eg.rationalfraction)Arationalfunctionisafunctionthatcanbewrittenasaquotientoftwopolynomialfunctions.Insymbols,thefunction: iscalledarationalfunction.systemfunction 系統(tǒng)函數(shù)transferfunction 傳遞函數(shù)WordsandExpressionsinterconnection n.互連constant n.常數(shù)delay n.延遲InterconnectionofLTIsystemsWordsandExpressionsformula n.公式expression 表達式equation 等式inequality 不等式LinearconstantcoefficientdifferenceequationWordsandExpressionsrecursive adj.遞歸的Incomputerprogramming,thetermrecursivedescribesafunctionormethodthatrepeatedlycalculatesasmallerpartofitselftoarriveatthefinalresult.Itissimilartoiteration,butinsteadofrepeatingasetofoperations,arecursivefunctionaccomplishesrepetitionbyreferringtoitselfinitsowndefinition.WordsandExpressionsinitial-restcondition 初始松弛條件Thedefinitionofinitialrestconditionforasystemingeneralisthatifx(t)=0fort<t0theny(t)=0fort<t0.

Fordiscretetimesystems,itbasicallysaysthat

theinputiszerouptoacertainpoint(orx[n]=0forn<n0),thentheoutputshouldbezerouptothesamepoint(ory[n]=0forn<n0).recurrence n.重現(xiàn)WordsandExpressionsblockdiagram 方框圖cascade n.級聯(lián)canonicformimplementation 規(guī)范形式實現(xiàn)Cascadestructurefora6th–ordersystemwithadirectformIIrealizationofeach2nd-ordersubsystemCanonicformimplementationofNth–orderLTIsystemBackgrounds36UCBerkeleyEE123.DigitalSignalProcessing/Courses/EE123/TextOutline37Representationsfordiscrete-timesystemDifferenceEquationImplementationBasicElementsBlockDiagramsRepresentationsfordiscrete-timesystemAnLTIsystemwitharationalsystemfunctionhasthepropertythattheinputandoutputsequencessatisfyalinearconstant-coefficientdifferenceequation.具有有理系統(tǒng)函數(shù)的線性時不變系統(tǒng)有這樣的性質(zhì)，即其輸入和輸出序列滿足線性常系數(shù)差分方程。38

39Representationsfordiscrete-timesystemSystemsdescribedbylinearconstant-coefficientdifferenceequationscanberepresentedbystructuresconsistingofaninterconnectionofthebasicoperationsofaddition,multiplicationbyaconstant,anddelay,theexactimplementationofwhichisdictatedbythetechnologytobeused.由線性常系數(shù)差分方程描述的系統(tǒng)能夠用由加法、常數(shù)乘法和延遲的基本運算互連而成的結(jié)構(gòu)來表示，它的真正實現(xiàn)則取決于所用的技術(shù)。40Representationsfordiscrete-timesystemBasicElementsThebasicelementsrequiredfortheimplementationofanLTIdiscrete-timesystemsareadders,multipliers,andmemoryforstoringdelayedsequencevaluesandcoefficients.實現(xiàn)線性時不變離散時間系統(tǒng)所需的基本單元是加法器、乘法器和存儲延遲序列值和系數(shù)的存貯器。41BasicElements42Figure5.1Blockdiagramsymbols.Additionoftwosequences.Multiplicationofasequencebyaconstant.Unitdelay.BlockDiagram43

Ablockdiagramcanberearrangedormodifiedinavarietyofwayswithoutchangingtheoverallsystemfunction.Eachappropriaterearrangementrepresentsadifferentcomputationalalgorithmforimplementingthesamesystem.在不改變整個系統(tǒng)函數(shù)的情況下，可以各種方式重新排列或修改框圖。每個適當(dāng)?shù)闹嘏疟硎居糜趯崿F(xiàn)相同系統(tǒng)的不同計算算法。44BlockDiagramSinceeachofthetwosystemsisanLTIsystem(assuminginitial-restconditionsforthedelayregisters),theorderinwhichthetwosystemsarecascadedcanbereversed,asshowninFigure5.3,withoutaffectingtheoverallsystemfunction.由于兩個系統(tǒng)都是線性時不變系統(tǒng)（假設(shè)延遲寄存器初始松弛），那么兩個系統(tǒng)在級聯(lián)中的次序就可以交換成如圖5.3所示，而不會影響總的系統(tǒng)函數(shù)。45BlockDiagram46Figure5.3Rearrangementofblockdiagramofmiddlefigure.BlockDiagramConsequently,thetwocanbecollapsedintoonechain,asindicatedinFigure5.4.Animplementationwiththeminimumnumberofdelayelementsiscommonlyreferredtoasacanonicformimplementation.因此，如圖5.4所示，兩者可以折疊成一條鏈。具有最小數(shù)量延遲單元的實現(xiàn)通常被稱為規(guī)范形式實現(xiàn)。47BlockDiagramBlockDiagram48Figure5.4ThedirectformIIorcanonicdirectformimplementation.5.3FilterDesignTechniquesWordsandExpressionsBackgroundsTextWordsandExpressionsbilineartransformation 雙線性變換法Thebilineartransformisaspecialcaseofaconformalmapping,oftenusedtoconvertatransferfunction

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

51WordsandExpressionsaliasing n.混疊WordsandExpressionspassband n.通帶stopband n.阻帶transition n.過渡帶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.濾波器是LTI系統(tǒng)中一類特別重要的系統(tǒng)。嚴(yán)格來說，選頻濾波器指的是讓輸入信號的某些頻率分量通過并完全抑制所有其他頻率分量的系統(tǒng)，但在更廣泛的定義下，任何相對于其他頻率分量修改特定頻率分量的系統(tǒng)都被稱為濾波器。55TypesofDigitalFiltersThedesignofdiscrete-timefilterscorrespondstodeterminingtheparametersofatransferfunctionordifferenceequationthatapproximatesadesiredimpulseresponseorfrequencyresponsewithinspecifiedtolerances.離散時間濾波器的設(shè)計即確定其傳遞函數(shù)或差分方程的參數(shù)，由此得到近似于規(guī)定容限內(nèi)的期望系統(tǒng)的脈沖響應(yīng)或頻率響應(yīng)。56TypesofDigitalFiltersDiscrete-timesystemsimplementedwithdifferenceequationsfallintotwobasiccategories:infiniteimpulseresponse(IIR)systemsandfiniteimpulseresponse(FIR)systems.用差分方程實現(xiàn)的離散時間系統(tǒng)分為兩類：無限脈沖響應(yīng)（IIR，也譯為無限沖激響應(yīng)）系統(tǒng)和有限脈沖響應(yīng)（FIR，也譯為有限沖激響應(yīng)）系統(tǒng)。57TypesofDigitalFiltersDesigningIIRfiltersimpliesobtaininganapproximatingtransferfunctionthatisrationalfunctionofz,whereasdesigningFIRfiltersimpliespolynomialapproximation.設(shè)計IIR濾波器意味著獲得近似的傳遞函數(shù)，該傳遞函數(shù)是z變量的有理函數(shù)，而設(shè)計FIR濾波器則意味著多項式逼近。58FilterdesigntechniquesWhendiscrete-timefiltersfirstcameintocommonuse,theirdesignwerebasedonmappingwell-formulatedandwell-understoodcontinuous-timefilterdesignstodiscrete-timedesignsthroughtechniquessuchasimpulseinvarianceandthebilineartransformation.當(dāng)離散時間濾波器首次普遍使用時，它們的設(shè)計是通過脈沖（沖激）響應(yīng)不變法和雙線性變換法等技術(shù)將精心設(shè)計且易于理解的連續(xù)時間濾波器設(shè)計映射到離散時間濾波器的設(shè)計。59FilterdesigntechniquesTheuseofthisproceduremaybemotivatedbyadesiretomaintaintheshapeoftheimpulseresponseorbytheknowledgethatifthecontinuous-timefilterisbandlimited,consequentlythediscrete-timefilterfrequencyresponsewillcloselyapproximatethecontinuous-timefrequencyresponse.使用本方法的出發(fā)點可能是希望保持沖激響應(yīng)的形狀，或者若已知連續(xù)時間濾波器是帶限的，那么離散時間濾波器的頻率響應(yīng)將非常接近連續(xù)時間濾波器的頻率響應(yīng)。60Filterdesigntechniques

61FilterdesigntechniquesThedesignoffiltersinvolvesthefollowingstages,thespecificationofthedesiredpropertiesofthesystem,theapproximationofthespecificationsusingacausaldiscrete-timesystem,andtherealizationofthesystem.濾波器的設(shè)計涉及以下步驟：給定系統(tǒng)所要求特性的技術(shù)指標(biāo)、用因果離散時間系統(tǒng)逼近這些技術(shù)指標(biāo)及實現(xiàn)該系統(tǒng)。62Filterdesigntechniques63Figure5.5Lowpassfiltertolerancescheme.FilterdesigntechniquesManyofthefiltersusinginpracticearespecifiedbyatoleranceschemewithnoconstraintsonthephaseresponse

otherthanthoseimposedimplicitlybyrequirementsofstabilityandcausality.在實踐中使用的許多濾波器是由容限方案指定的，除了穩(wěn)定性和因果關(guān)系要求隱含施加的約束之外，對相位響應(yīng)沒有任何約束。64FilterdesigntechniquesForthedesignofFIRfilters,windowfunctionmethodandoptimumapproximationmethodareapplied.ThechoicebetweenanFIRfilterandanIIRfilterdependsontheimportancetothedesignproblemoftheadvantagesofeachtype.IIRfilters,forexample,havetheadvantagethatavarietyoffrequency-selectivefilterscanbedesignedusingclosed-formdesignformulas.FIR濾波器的設(shè)計采用了窗函數(shù)法和最優(yōu)逼近法。FIR濾波器和IIR濾波器之間的選擇取決于每種類型的優(yōu)點對設(shè)計問題的重要性。例如，IIR濾波器的優(yōu)點是，可以使用閉合形式的設(shè)計公式來設(shè)計各種頻率選擇性濾波器。65FilterdesigntechniquesAlthoughthewindowmethodisstraightforwardtoapply,someiterationmaybenecessarytomeetaprescribedspecification.TheParks-McClellanalgorithmleadstolowerorderfiltersthanthewindowmethoddoes,andbothmethodscanbeimplementedonapersonalcomputeroraworkstation.盡管窗函數(shù)法應(yīng)用起來很簡單，但為滿足規(guī)定的技術(shù)指標(biāo)，可能需要進行一些迭代。Parks-McClellan算法比窗函數(shù)法設(shè)計的濾波器階次低，并且這兩種方法都可以在個人計算機或工作站上實現(xiàn)。66EconomicConcernsClearly,thefinalchoicewillmostoftenbemadebyengineeringjudgementonsuchquestionsastheformulationofthespecifications,themethodofimplementationofthefilter,andthecomputationalfacilitiesandsof