通信與電子信息專業(yè)英語 課件 Unit 4 Signals and Systems

Unit4SignalsandSystems4.1IntroductiontoSignals

4.2FrequencyResponseofLTISystems

4.3SamplingTheorem4.1IntroductiontoSignalsWordsandExpressionsBackgroundsTextWordsandExpressionsfunction n.函數(shù)variable n.變量Themoderndefinitionoffunctionwasfirstgivenin1837bytheGermanmathematicianPeterDirichlet:Ifavariableyissorelatedtoavariablexthatwheneveranumericalvalueisassignedtox,thereisaruleaccordingtowhichauniquevalueofyisdetermined,thenyissaidtobeafunctionoftheindependentvariablex，symbolizedasy=f(x).4WordsandExpressionscontinuous-timesignal 連續(xù)時間信號discrete-timesignal 離散時間信號5Discrete-timesignalcreatedfromacontinuoussignalby

samplingUnit-StepFunctionunitimpulsefunctionpulsefunctionWordsandExpressionssignaltransformation 信號變換timeshift 時移6WordsandExpressionsdelay v.滯后advance v.超前7delayedsignal

advancedsignal

WordsandExpressionsradar n.雷達(dá)sonar n.聲吶8Radar

(originally

acronym

for

radiodetectionandranging)

isadetectionsystemthatuses

radiowaves

todeterminethedistance(ranging),angle,and

radialvelocity

ofobjectsrelativetothesite.Itcanbeusedtodetect

aircraft,

ships,

spacecraft,

guidedmissiles,

motorvehicles,

weatherformations,and

terrain.

Sonar

(soundnavigationandranging)isatechniquethatuses

sound

propagation(usuallyunderwater,asin

submarinenavigation)to

navigate,measuredistances(ranging),communicatewithordetectobjectsonorunderthesurfaceofthewater,suchasothervessels.WordsandExpressionsreceiver n.接收機(jī)medium n.媒介

propagation n.傳播

9AbundleofopticalfiberA

transmissionmedium

isasystemorsubstancethatcanmediatethe

propagation

of

signals

forthepurposesof

telecommunication.WordsandExpressionstimereversal 時間變量的翻轉(zhuǎn)timescaling 時間變量的尺度變換10WordsandExpressionsperiodic adj.周期的period n.周期sinusoidalsignal 正弦信號11Acontinuous-timeperiodicsignal.Asinusoidalsignal.Backgrounds12SignalsAndSystems/courses/6-003-signals-and-systems-fall-2011/TextOutlineIntroductiontoSignalscontinuoussignalsdiscretesignalsSignalTransformationinTimeDomainshiftreversalscaling13IntroductiontoSignalsSignalsarerepresentedmathematicallyasfunctionsofoneormoreindependentvariables.數(shù)學(xué)上信號表示為一個或多個自變量的函數(shù)。14Anexampleofadiscrete-timesignal:TheweeklyDow-JonesstockmarketindexfromJanuary5,1929,toJanuary4,1930.IntroductiontoSignalsForexample,aspeechsignalcanberepresentedmathematicallybyacousticpressureasafunctionoftime,andapicturecanberepresentedbybrightnessasafunctionoftwospatialvariables.例如在數(shù)學(xué)上，語音信號可表示為聲壓隨時間變化的函數(shù)，圖像可用亮度隨二維空間變量變化的函數(shù)來表示。15ImagesoftheCrabPulsar(inthecenterofeachimage)coveringtheelectromagneticspectrum.(CourtesyofNASA.)IntroductiontoSignalsOntheotherhand,discrete-timesignalsaredefinedonlyatdiscretetimes,andconsequently,forthesesignals,theindependentvariabletakesononlyadiscretesetofvalues.另一方面，離散時間信號僅在離散時間定義，因此，對這些信號，自變量僅具有一組離散值。16TransformationinTimeDomainAsimpleandveryimportantexampleoftransformingtheindependentvariableofasignalisatimeshift.時移是信號自變量變換的一個簡單且重要的例子。17Discrete-timesignalsrelatedbyatimeshift.Inthisfiguren0>0,sothatx[n-n0]isadelayedversionofx[n](i.e.,eachpointinx[n]occurslaterinx[n-n0]).Continuous-timesignalsrelatedbyatimeshift.Inthisfiguret0<0,sothatx(t–t0)isanadvancedversionofx(t)(i.e.,eachpointinx(t)occursatanearliertimeinx(t–t0)).TransformationinTimeDomainInthiscase,thedifferenceinpropagationtimefromthepointoforiginofthetransmittedsignaltoanytworeceiversresultsinatimeshiftbetweenthesignalsatthetworeceivers.在此情況下，從發(fā)射信號原始位置到任意兩個接收機(jī)之間的傳輸時間差異會導(dǎo)致兩個接收機(jī)中信號的時移。18TransformationinTimeDomain

194.2FrequencyResponseofLTISystemsWordsandExpressionsBackgroundsTextWordsandExpressionslineartime-invariantsystem,LTIsystem 線性時不變系統(tǒng)linear:Asystemislinearifandonlyifitsatisfiesthesuperpositionprinciple,orequivalentlyboththeadditivityandhomogeneityproperties,withoutrestrictions.time-invariant:Atime-invariantsystemhasthepropertythatacertaininputwillalwaysgivethesameoutput,withoutregardtowhentheinputwasappliedtothesystem.WordsandExpressionstime-domaincharacteristic 時域表征frequency-domaincharacteristic 頻域表征WordsandExpressions詞匯拓展：表示特征、性質(zhì)、特性的單詞characteristicproperty:propertyofFTfeature:featureextractionsignature:明顯特征、識別標(biāo)志

TheframeworkfordeeplocalfeatureextractionpipelineWordsandExpressionsconvolution n.卷積differentialanddifferenceequations 微分與差分方程WordsandExpressions詞匯拓展：convolution/deconvolution 卷積/解卷積coding/decoding 編碼/解碼compression/decompression 壓縮/解壓correlation/decorrelation 相關(guān)/去相關(guān)cypher/decipher 譯碼/破譯

modulation/demodulation 調(diào)制/解調(diào)WordsandExpressionsfiltering n.濾波Filter:adeviceorprocessthatremoves

someunwantedcomponentsorfeaturesfroma

signal.

WordsandExpressionsrealandimaginarycomponents 實部和虛部分量magnitude n.幅度phase n.相位

WordsandExpressionsFouriertransform 傅里葉變換Fouriertransform 傅里葉變換Fourierseries 傅里葉級數(shù)DiscretetimeFouriertransform 離散時間傅里葉變換DiscreteFouriertransform 離散傅里葉變換FastFouriertransform 快速傅里葉變換WordsandExpressionsfrequencyresponse 頻率響應(yīng)impulseresponse 沖激（脈沖）響應(yīng)WordsandExpressionsgain n.增益phaseshift 相移Illustrationofphaseshift.Thehorizontalaxisrepresentsanangle(phase)thatisincreasingwithtime.WordsandExpressionsmagnitudeandphasedistortion 幅度和相位失真In

signalprocessing,

groupdelay

and

phasedelay

aredelaytimesexperiencedbyasignal'svarious

frequencycomponents

whenthesignalpassesthroughasystemthatis

lineartime-invariant

(LTI),suchasa

microphone,

coaxialcable,

amplifier,

loudspeaker,

telecommunicationssystem

or

ethernetcable.Thesedelaysaregenerallyfrequencydependent.This

meansthatdifferentfrequencycomponentsexperiencedifferentdelays,whichcause

distortion

ofthesignal's

waveform

asitpassesthroughthesystem.WordsandExpressionsslope n.斜率cascade n.級聯(lián)Bodeplot 伯德圖AtypicalBodeplot.seriesorcascadeinterconnectionoftwosystemsparallelinterconnectionoftwosystems.Backgrounds33CORNELLECEOPENCOURSEWAREECE3250MATHEMATICSOFSIGNALANDSYSTEMANALYSIS/courses/ece-3250-mathematics-of-signal-and-system-analysis/TextOutline34IntroductionFourierTransformFrequencyResponseofLTISystemBodePlotIntroductionThefrequency-domaincharacterizationofanLTI(lineartime-invariant)systemintermsofitsfrequencyresponserepresentsanalternativetothetime-domaincharacterizationthroughconvolution.線性時不變系統(tǒng)的以頻率響應(yīng)為代表的頻域表征是以卷積為代表的時域表征的替代方法。35IntroductionInanalyzingLTIsystems,itisoftenparticularlyconvenienttoutilizethefrequencydomainbecausedifferentialanddifferenceequationsandconvolutionoperationsinthetimedomainbecomealgebraicoperationsinthefrequencydomain.在分析LTI系統(tǒng)時，利用頻域通常特別方便，因為時域中的微分方程和差分方程以及卷積運算變成了頻域中的代數(shù)運算。36FourierTransform

37

38FrequencyResponseofLTISystemFrequencyResponseofLTISystemThus,theeffectthatanLTIsystemhasontheinputis

tochangethecomplexamplitudeofeachofthefrequencycomponentsofthesignal.因此，LTI系統(tǒng)對輸入的影響是改變信號的每個頻率分量的復(fù)振幅。39FrequencyResponseofLTISystem

40FrequencyResponseofLTISystem

41FrequencyResponseofLTISystemThechangesinthemagnitudeandphasethatresultfromtheapplicationofaninputtoanLTIsystemmaybeeitherdesirable,iftheinputsignalismodifiedinausefulway,orundesirable,iftheinputischangedinanunwantedmanner.如果以有意義的方式改變輸入信號，則由于向線性時不變系統(tǒng)應(yīng)用輸入信號而導(dǎo)致的幅度和相位變化可能是所希望的，否則是不希望的。42BodePlotIngraphicallydisplayingcontinuous-timeordiscrete-timeFouriertransformsandsystemfrequencyresponsesinpolarform,itisoftenconvenienttousealogarithmicscaleforthemagnitudeoftheFouriertransform.以極坐標(biāo)形式展示連續(xù)時間或離散時間傅里葉變換和系統(tǒng)頻率響應(yīng)時，對傅里葉變換的幅度采用對數(shù)刻度往往是方便的。43BodePlotConsequently,ifwehaveagraphofthelogmagnitudeandphaseoftheFouriertransformoftheinputandthefrequencyresponseofanLTIsystem,theFouriertransformoftheoutputisobtainedbyaddingthelog-magnitudeplotsandbyaddingthephaseplots.因此，如果我們已知線性時不變系統(tǒng)輸入的傅里葉變換和頻率響應(yīng)的對數(shù)幅度和相位圖，那么通過將兩者的對數(shù)幅度圖相加和它們的相位圖相加可獲得輸出的傅里葉變換。444.3SamplingTheoremWordsandExpressionsBackgroundsTextWordsandExpressionssamplingtheorem 采樣定理Samplingtheorem:atheoreminthefieldof

signalprocessing

whichservesasafundamentalbridgebetween

continuous-timesignals

and

discrete-timesignals.

Itestablishesasufficientconditionfora

samplerate

thatpermitsadiscretesequenceof

samples

tocapturealltheinformationfromacontinuous-timesignaloffinite

bandwidth.WordsandExpressionsinterval n.區(qū)間，時間間隔impulsetrain 沖激串WordsandExpressionssamplingperiod 采樣周期samplingfrequency 采樣頻率WordsandExpressionssuperposition n.疊加overlap n.交疊，重疊aliasing n.圖形失真；聲音失真aliasingdistortion 混疊失真aliasingeffect 混疊效應(yīng)spectralaliasing 頻譜混疊low-passfilter 低通濾波器WordsandExpressionscut-offfrequency 截止頻率Thecutofffrequencyorcornerfrequencyinelectronicsisthefrequencyeitheraboveorbelowwhichthepoweroutputofacircuit,suchasaline,amplifier,orelectronicfilter(e.g.ahighpassfilter)hasfallentoagivenproportion(mostlyone-halfthepassbandpower,alsoreferredtoasthe3dB)ofthepowerinthepassband.WordsandExpressionsband-limitedsignal 帶限信號WordsandExpressionsinformationtheory 信息論Informationtheory:thescientificstudyofthe

quantification,

storage,and

communication

of

digital

information，fundamentallyestablishedbytheworksof

HarryNyquist

and

RalphHartley,inthe1920s,and

ClaudeShannon

inthe1940s.Thefieldisattheintersectionof

probabilitytheory,

statistics,

computerscience,

statisticalmechanics,

informationengineering,and

electricalengineering.WordsandExpressionsClaudeElwoodShannon

(April30,1916–February24,2001)wasanAmerican

mathematician,

electricalengineer,

computerscientist

and

cryptographer

knownasthe"fatherof

informationtheory".In1948,thepromisedmemorandumappearedasAMathematicalTheoryofCommunication,anarticleintwopartsintheJulyandOctoberissuesofthe

BellSystemTechnicalJournal.Thisworkfocusesontheproblemofhowbesttoencodethemessageasenderwantstotransmit.Shannondeveloped

informationentropy

asameasureofthe

information

contentinamessage,whichisameasureofuncertaintyreducedbythemessage.Insodoing,heessentiallyinventedthefieldof

informationtheory.Backgrounds54PurdueUniversityEE301SignalsandSystemsSpring2024/~mikedz/ee301/ee301.htmlTextSamplingtheoremStatementofsamplingtheoremReconstructionofcontinuoussignals55Samplingtheorem56Undercertainconditions,acontinuous-timesignalcanbecompletelyrepresentedbyandrecoverablefromknowledgeofitsvalues,orsamples,atpointsequallyspacedintime.在一定條件下，一個連續(xù)時間信號完全可以用該信號在等時間間隔點上的值或樣本來表示，并且可以用這些樣本值把該信號全部恢復(fù)出來。Samplingtheorem57Whenthesesamplesareviewedinsequenceatasufficientlyfastrate,weperceiveanaccuraterepresentationoftheoriginalcontinuouslymovingscene.當(dāng)以足夠快的速度來看這些時序樣本時，我們就會感覺到是原來連續(xù)活動景象的重現(xiàn)。Thisanimationmovesat10framespersecond.Dependingonthefrequencyofflash,theelementappearsmotionlessorrotatinginreversedirection(stroboscopiceffect:頻閃效應(yīng))Samplingtheorem58

59SamplingtheoremImpulse-trainsampling.

Samplingtheorem60

Samplingtheorem61

Samplingtheorem62

SamplingtheoremExactrecoveryofaCTsignalfromitssamplesusinganideallowpassfilter:(a)systemforsamplingandreconstruction;(b)representativespectrumforx(t);(c)correspondingspectrumforxp(t);(d)ideallowpassfiltertorecoverX(jw)fromXp(jw);(e)spectrumOfxr(t).Samplingtheorem64

Samplingtheorem65

HarryNyquistAsanengineeratBellLaboratories,Nyquistdidimportantworkonthermalnoise("Johnson–Nyquistnoise"),

thestabilityof

feedback

amplifiers,telegraphy,

facsimile,television,andotherimportantcommunicationsproblems.With

HerbertE.Ives,hehelpedtodevelopAT&T'sfirstfacsimilemachinesthatweremadepublicin1924.In1932,hepublishedaclassicpaperonstabilityoffeedbackamplifiers.

The

Nyquiststabilitycriterion

cannowbefoundinalltextbooksonfeedbackcontroltheory.HarryNyquistHisearlytheoreticalworkondeterminingthebandwidthrequirementsfortransmittinginformationlaidthefoundationsforlateradvancesby

ClaudeShannon,whichledtothedevelopmentof

informationtheory.Inparticular,Nyquistdeterminedthatthenumberofindependentpulsesthatcouldbeputthroughatelegraphchannelperunittimeislimitedtotwicethe

bandwidth

ofthechannel,andpublishedhisresultsinthepapers

Certainfactorsaffectingtelegraphspeed

(1924)

and

CertaintopicsinTelegraphTransmissionTheory

(1928).

Thisruleisessentiallya

dual

ofwhatisnowknownasthe

Nyquist–Shannonsamplingtheorem.Exercises681.Matchtheterms(1)-(6)withthedefinitionsA-F.1.signalsA.systemwhichhaspropertiesoflinearityandtime-invariance2.lineartime-invariantsystemB.