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Chapter3SignalSystem SignalProcessing 3 1SignalandSystem3 2DigitalSignalProcessing3 3SpeechSignalProcessing TEXT3 1SignalandSystem Simplyintroductionofthemathematicalrepresentationsofcontinuous timeanddiscrete timesignalsandsystems andtheconceptsofsignalenergyandpower 1 Continuous timeanddiscrete timesignals2 Continuous timeanddiscrete timesystems3 Somepropertiesofdigitalsignalsystem4 Signalenergyandpower Terminology aeronauticsn 航空学 航空术astronauticsn 太空航空学seismologyn 地震学meteorologicadj 气象的 气象学的profilen 剖面 侧面 外形 轮廓conventionn 大会 协定 习俗 惯例terminologyn 术语学electromechanicaladj 机 电动机械的 机电的 电机的automotiveadj 汽车的 自动推进的vehiclen 交通工具 车辆high fidelity高保真tonen 音调 音质 语调 1 Continuous timeanddiscrete timesignals Signalsarerepresentedmathematicallyasfunctionsofoneormoreindependentvariables eg 1 aspeechsignalcanberepresentedmathematicallybyacousticpressureasafunctionoftime eg 2apicturecanberepresentedbybrightnessasafunctionoftwospatialvariables Todistinguishbetweencontinuous timeanddiscrete timesignals wewillusethesymbolttodenotethecontinuous timeindependentvariablewhichisenclosedinparentheses andntodenotethediscrete timeindependentvariableinbrackets Illustrationsofacontinuous timesignalandadiscrete timesignalareshowninFig 3 4 a b Fig 3 4Graphicalrepresentationsof a continuous timeand b discrete timesignals Physicalsystemsinthebroadestsenseareaninterconnectionofcomponents devices orsubsystems Incontextrangingfromsignalprocessingandcommunicationstoelectromechanicalmotors automotivevehicles andchemical processingplants asystemcanbeviewedasaprocessinwhichinputsignalsare 2 Continuous timeanddiscrete timesystems transformedbythesystemorcausethesystemtorespondinsomeway resultinginothersignalsasoutputs Forexample ahigh fidelitysystemtakesarecordedaudiosignalandgeneratesareproductionofthatsignal Ifthehi fisystemhastonecontrols wecanchangethetonalqualityofthereproducedsignal Itisimportanttonotethatthediscrete timesignalsdefinedonlyforintegervaluesoftheindependentvariable Acontinuous timesystemisasysteminwhichcontinuous timeinputsignalsareappliedandresultincontinuous timeoutputsignals AsinFigure3 1 5 a wherex t istheinput y t istheoutput andh t isthesystemimpulseresponse Similarly adiscrete timesystem thatis asystemthattransformsdiscrete timeinputsintodiscrete timeoutputs isdepictedasinFigure3 1 5 b Wherex n istheinput y n istheoutput andh n isthesystemunitsampleresponse Wecanbringcontinuous timeanddiscrete timesystemstogetherthroughtheconceptofsampling andwecandevelopsomeinsightsintotheuseofdiscrete timesystemstoprocesscontinuous timesignalsthathavebeensampled Atpresent manydigitalsignalprocessingmethodshavebeenwidelyusedinscienceandtechnologyfields Sowetakedigitalsignalsystemforexample somesystempropertiesaredescribedinnextsection 3 Somepropertiesofdigitalsignalsystem ThelinearityofasystemTimeinvarianceofasystemisdefinedas Linearityandtimeinvarianceareindependentproperties Communtative Associative Distributive 4 Signalenergyandpower Signalswithfinitetotalenergy i e signalsforwhichSuchasignalmusthavezeroaveragepower signalsisthosewithfiniteaveragepower signalsisthesignalsforwhichneither nor arefinite EXERCISES 1 PleasetranslatethefollowingwordsandphrasesintoChinese 2 PleasetranslatethefollowingwordsandphrasesintoEnglish TEXT3 2DigitalSignalProcessing Introduction2 FourierAnalysis3 FIRdigitalfilterdesign4 WindowFunctions Terminology fidelityn 保真度 收音机 录音设备等的 逼真度 保真度 重现精度sensoryadj 感觉的 感官的seismicadj 地 地震的vibrationsn 振动 颤动 摇动 摆动storagen 贮藏 量 贮藏库 存储superpositionn 重叠 重合 叠合ubiquitousadj 到处存在的 同时 普遍存在的utilityn 效用 有用 symmetryn 对称 匀称weightfunction权值函数approximatev 近似 接近 接近 约计integraln 数学 积分 完整 部分sparsematrice稀疏矩阵invariantadj 无变化的 不变的Fourierseries傅立叶级数recursiveadj 回归的 递归的evenfunction偶函数intervaln 间隔non recursive非回归的 非递归的finite duration有限长时间 physicaladj 自然的 物理的delayv 耽搁 延迟 延期 迟滞re indexing改变符号oscillatoryadj 摆动的ripplen 波纹transitionn 转变 转换 跃迁 过渡 变调Gibbsphenomenon Gibbs现象sub optimumadj 未达最佳标准的mainloben 主瓣sideloben 旁瓣attenuationn 衰减 IntroductionDigitalsignalprocessingisdistinguishedfromotherareasincomputersciencebytheuniquetypeofdataituses signals Inengineeringcontext signalsarecarriersofinformation bothusefulandunwanted Thereforeextractingorenhancingtheusefulinformationfromamixofconflictinginformationisasimplestformofsignalprocessing Thedistinctionbetweenusefulandunwantedinformationisoftensubjectiveaswellasobjective Hencesignalprocessingtendstobeapplicationdependent Fourieranalysisandfilterdesignarethemethodsoftenusedinsignalprocessing Thus theirprinciplesaredescribedsimplyasfollowings 2 FourierAnalysis TheFouriertransform sutilityliesinitsabilitytoanalyzeasignalinthetimedomainforitsfrequencycontent Thetransformworksbyfirsttranslatingafunctioninthetimedomainintoafunctioninthefrequencydomain ThediscreteFouriertransform DFT estimatestheFouriertransformofafunctionfromafinitenumberofitssampledpoints Thesampledpointsaresupposedtobetypicalofwhatthesignallookslikeatallothertimes Ifisanonperiodicsignal thesummationoftheperiodicfunctions suchassineandcosine doesnotaccuratelyrepresentthesignal Youcouldartificiallyextendthesignaltomakeitperiodicbutitwouldrequireadditionalcontinuityattheendpoints ThewindowedFouriertransform WFT isonesolutiontotheproblemofbetterrepresentingthenonperiodicsignal TheWFTcanbeusedtogiveinformationaboutsignalssimultaneouslyinthetimedomainandinthefrequencydomain Toapproximateafunctionbysamples andtoapproximatetheFourierintegralbythediscreteFouriertransform requiresapplyingamatrixwhoseorderisthenumbersamplepointsn Sincemultiplyinganmatrixbyavectorcostsontheorderofarithmeticoperations theproblemgetsquicklyworse asthenumberofsamplepointsincreases However ifthesamplesareuniformlyspaced thentheFouriermatrixcanbefactoredintoaproductofjustafewsparsematrices andtheresultingfactorscanbeappliedtoavectorinatotaloforderarithmeticoperations Thisistheso calledfastFouriertransformorFFT 3 FIRdigitalfilterdesign Adigitalfilterisamathematicalalgorithmimplementedinhardware firmware andsoftwarethatoperatesonadigitalinputsignaltoproduceadigitaloutputsignalforachievingfilteringobjectives Adigitalfiltercanbeclassifiedasbeinglinearornonlinear timeinvariantorvarying Thissectionisfocusedonthedesignoflinear time invariant LTI finiteimpulseresponse FIR filters AvarietyoftechniqueshavebeenproposedforthedesignofFIRfilters Therearetwodirectdesignmethodswhichareoftenused ThefirstmethodisbasedontruncatingtheFourierseriesrepresentationofthedesiredfrequencyresponse ThemethodoffersaverysimpleandflexiblewayofcomputingFIRfiltercoefficients butitdoesnotallowthedesigneradequatecontroloverthefilterparameters Thesecondmethodisbasedonspecifyingequallyspacedfrequencysamplesofthefrequencyresponseofthedesiredfilter Themainattractionofthefrequency samplingmethodisthatitallowsrecursiverealizationofFIRfilters whichcanbecomputationallyefficient However itlacksflexibilityinspecifyingorcontrollingfilterparameters TheFourierseries window methodisdiscussedinasfollowings 4 WindowFunctions Inpractice thelengthofthewindowshouldbeassmallaspossibleinordertoreducethecomputationalcomplexityoftheFIRfilter Thereforewehavetousesub optimumwindowsthathavethefollowingproperties 1 Theyareevenfunctionsaboutn 0 2 Theyarezerointherange 3 Theirfrequencyresponseshaveanarrowmainlobeandsmallsidelobesassuggestedbyeq 3 36 EXERCISES PleasetranslatethefollowingwordsandphrasesintoChinese PleasetranslatethefollowingwordsandphrasesintoEnglish Answerthefollowingquestionsaccordingtothetext WhatisthefastFouriertransform Whichtwomethodsareoftenusedindigitalfilterdesigning PleasetelluswhatistheGibbsphenomenon TEXT3 3SpeechSignalProcessing 1 TheSpeechSignal2 SignalProcessing3 DigitalSignalProcessing4 DigitalSpeechProcessing Terminology characterizevt 表现 的特色 刻画的 性格abstractadj 抽象的 深奥的 理论的ultimatelyadv 最后 终于 根本 基本上articulatoryadj 分节的 关节的articulatorn 发音之人或物 音节分明之人 intrinsicallyadj 本质地 固有地phonemen 语 音位 音素concatenationn 串联 链接singleout挑选 counterpartn 副本 极相似的人或物 配对物catalystn 催化剂virtuen 德行 美德 优点 功效 效力dedicatedadj 专用的 为某一特定的用途或功能而设计的concomitantadj 伴随的 n 伴随物encryptionn 计 加密术 密码术queryv 询问 表示怀疑Touch Toneadj 按键式的transactionn 办理 交易 事务 处理事务 Inconsideringtheprocessofspeechcommunication itishelpfultobeginbythinkingofamessagerepresentedinsomeabstractforminthebrainofthespeaker Throughthecomplexprocessofproducingspeech theinformationinthatmessageisultimatelyconvertedtoanacousticsignal 1 TheSpeechSignal Themessageinformationcanbethoughtofasbeingrepresentedinanumberofdifferentwaysintheprocessofspeechproduction Forexample themessageinformationisfirstconvertedintoasetofneuralsignalswhichcontrolthearticulatorymechanism thatis themotionsofthetongue lips vocalcords etc Thearticulatorsmoveinresponsetotheseneuralsignalstoperformasequenceofgestures theresultofwhichisanacousticwaveformwhichcontainstheinformationintheoriginalmessage Inspeechcommunicationsystems thespeechsignalistransmitted stored andprocessedinmanyways Ingeneral therearetwomajorconcernsinanysystem oneispreservationofthemessagecontentinthespeechsignal Anotherisrepresentationofthespeechsignalinaformthatisconvenientfortransmissionorstorage orinaformthatisflexiblesothatmodificationmaybemadetothespeechsignalwithoutseriouslydegradingthemessagecontent Processingofspeechsignalsgenerallyinvolvestwotasks First itisavehicleforobtainingageneralrepresentationofaspeechsignalineitherwaveformorparametricform 2 SignalProcessing Second signalprocessingservesthefunctionofaidingintheprocessoftransformingthesignalrepresentationintoalternateformswhicharelessgeneralinnature butmoreappropriatetospecificapplications Fig 3 22Generalviewofinformationmanipulationandprocessing Signalprocessinginvolvesfirstobtainingarepresentationofthesignalbasedonagivenmodelandthentheapplicationofsomehigherleveltransformationinordertoputthesignalintoamoreconvenientform Thelaststepintheprocessistheextractionandutilizationofthemessageinformation Thisstepmaybeperformedeitherbyhumanlistenersorautomaticallybymachines Bywayofexample asystemwhosefunctionistoautomaticallyidentifyaspeakerfromagivensetofspeakersmightuseatime dependentspectralrepresentationofthespeechsignal Onepossiblesignaltransformationwouldbetoaveragespectraacrossanentiresentence comparetheaveragespectrumtoastoredaveragedspectrumtemplateforeachpossiblespeaker andthenbasedonaspectralsimilaritymeasurementchoosetheidentityofspeaker Forthisexamplethe information inthesignalistheidentityofthespeaker Therepresentationofspeechsignalsindigitalformis ofcourse offundamentalconcern Inthisregardweareguidedbythewell knownsamplingtheoremwhichstatesthatabandlimitedsignalcanberepresentedbysamplestakenperiodicallyintime providedthatthesamplesaretakenatahighenoughrate 3 DigitalSignalProcessing Therearemanyotherreasonsforusingdigitaltechniquesinspeechcommunicationsystems Forexample ifsuitablecodingisused speechindigitalformcanbereliablytransmittedoververynoisychannels Also ifthespeechsignalisindigitalformitisidenticaltodataofotherforms Thusacommunicationsnetworkcanbeusedtotransmitbothspeechanddatawithnoneedtodistinguishbetweenthemexceptinthedecoding Also withregardtotransmissionofvoicesignalsrequiringsecurity thedigitalrepresentationhasadistinctadvantageoveranalogsystems Forsecrecy theinformationbitscanbescrambledinamannerwhichcanultimatelybeunscrambledatthereceiver Fortheseandnumerousotherreasonsdigitaltechniquesarebeingincreasinglyappliedinspeechcommunicationproblems 4 DigitalSpeechProcessing Inconsideringtheapplicationofdigitalsignalprocessingtechniquestospeechcommunicationproblems itishelpfultofocusonthreemaintopics therepresentationofspeechsignalsindigitalform theimplementationofsophisticatedprocessingtechniques andtheclassesofapplicationswhichrelyheavilyondigitalprocessing Fig 3 23Representationsofspeechsignals AsshowninFig 3 23 theserepresentationscanbeclassifiedintotwobroadgro

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