通信原理(英文版)4

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1、Chapter4Digitiationofanalogsignal4.1IntroductionTwocategoriesofinformationsources:analogsignal,digitalsignalThreestepsofA/Dconversion:sampling,quantization,codingMostpopularA/Dconversionmethod:PulseCodeModulation(PCM)1s(t)Analogsignal4.2Samplingofanalogsignal4.2.1Samplingoflow-passanalogsignalUs

2、uallysamplingatequaltimeintervalTTheoretically,samplingprocess＝periodicalunitimpulseanalogsignalPractically,samplingprocess＝periodicalnarrowpulseanalogsignalSamplingtheorem:Ifthehighestfrequencyofacontinuousanalogsignals(t)islessthanfH,andifitissampledbyperiodicimpulseswithintervaltimeT1/2fH,

3、thens(t)canbecompletelydecidedbythesesamples.2ProofofsamplingtheoremLet:s(t)－signalwithhighestfrequencylessthanfHT(t)－periodicalunitimpulsewithrepetitionperiodTandrepetitionfrequencyfs=1/T,thenthesampledsignalis:LettheFouriertransformofsk(t)isSk(f),thenwhere,Sk(f)－spectrumofsk(t)S(f)－spectrumof

4、s(t)(f)－spectrumofT(t)(f)isthefrequencyspectrumofperiodicalunitimpulse,itcanbefoundas3SubstitutingintoobtainTheaboveequationshowsthatspectrumSk(f)ofthesampledsignalisthesuperpositionofinfinitespectraS(f)withfrequencyintervalfs,sinceS(f-nfs)istheresultofdisplacementnfsofthesignalfrequencyspe

5、ctrumS(f)onthefrequencyaxis.Thehighestfrequencyofsignals(t)hasbeenassumedlessthanfH,thereforeiffrequencyintervalfs2fH,theneachdisplacedspectrumS(f)oftheoriginalsignalcontainedinSk(f)isnotsuperposedwitheachother,asshowninthefigure.ThusfrequencyspectrumS(f)ofsignals(t)canbeseparatedfromSk(f),ands

6、(t)canbeeasilyobtainedfromS(f),i.e.theoriginalsignalcanberestoredfromthesampledsignal.4Here,theconditionofrestorationoftheorigialsignalis2fHiscalledNyquistsamplingrate.ThecorrespondingsmallestsamplingtimeintervaliscalledNyquistsamplinginterval.5Methodofrestorationoforiginalsignalfromsampledsigna

7、l:Frequencydomain:Whenfs2fH,theoriginalsignalcanbeseparatedfromthesampledsignalbyanideallow-passfilerwithcut-offfrequencyfH.Timedomain:Whentheideallow-passfilterisexcitedbythesampledpulsesequence,theoutputofthefilteristhesu