CommSystemChapter3

CommunicationSystemsChapter3PulseModulationCommunicationSystemsPulseModulation2contents•Sampling•Pulse-amplitudemodulationPAM•Quantization•Pulse-codemodulationPCM•Time-divisionmultiplexingTDM•Digitalmultiplexers•ImprovedPCM:DM,DPCM,ADPCM•MPEG-1/audiocodingstandardCommunicationSystemsPulseModulation33.1Introduction•Continuous-wavemodulation(CW)•Pulsemodulation(PM)Thecarrierconsistsofaperiodicsequenceofrectangularpulses.someparameterofapulsetrainisvariedwiththemessagesignal.Pulseparameters:1.Amplitude2.Position3.Width/durationCommunicationSystemsPulseModulation4PulsemodulationtypesPulse-amplitudemodulation(PAM)Pulse-durationmodulation(PDM)Pulse-positionmodulation(PPM)Pulsecodemodulation(PCM)DPCM,ADPCM,MAnalogpulsemodulationDigitalpulsemodulationCommunicationSystemsPulseModulation53.2SamplingProcessSampling:ananalogsignalisconvertedintoacorrespondingsequenceofsamples.Ts:samplingperiodfs=1/Ts:samplingrateinstantaneoussampledversionoftheanalogsignalAnalogsignalInstantaneoussamplingidealsamplingCommunicationSystemsPulseModulation6Question:howtochoosethesamplingrateproperlysothatthesequenceofsamplesuniquelydefinetheoriginalanalogsignal?Samplingtheoremanswersthisquestion.CommunicationSystemsPulseModulation7IdealsamplingprocessIdealsampledsignal:Fourier-transformpairs:()()FTgtGfThen()()()3.2FTssmgtGffGfmf()()()()()3.1sssnngtgttnTgnTtnTmssmssnsmfffTmfTnTt)()1(1)(g(t))(tg()stnT抽样过程的时频域对比CommunicationSystemsPulseModulation9Reconstructionoftheoriginalsignalg(t)InterpolationformulaInterpolationfunctionsin(2)()()()sin(2)3.92(2)2nnnWtnngtggcWtnWWtnWt©2000,JohnWiley&Sons,Inc.Haykin/CommunicationSystems,4thEdFigure3.2(a)Spectrumofastrictlyband-limitedsignalg(t).(b)Spectrumofthesampledversionofg(t)forasamplingperiodTs=1/2W.©2000,JohnWiley&Sons,Inc.Haykin/CommunicationSystems,4thEdFigure3.3(a)Spectrumofasignal.(b)Spectrumofanundersampledversionofthesignalexhibitingthealiasingphenomenon.©2000,JohnWiley&Sons,Inc.Haykin/CommunicationSystems,4thEdFigure3.4(a)Anti-aliasfilteredspectrumofaninformation-bearingsignal.(b)Spectrumofinstantaneouslysampledversionofthesignal,assumingtheuseofasamplingrategreaterthantheNyquistrate.(c)Magnituderesponseofreconstructionfilter.抽样信号的频谱Gs(f)是无数间隔频率为fs的原信号频谱G(f)相叠加而成。Samplingtheorem•抽样定理：设一个连续模拟信号m(t)中的最高频率W，则以间隔时间为T1/2W的周期性冲激脉冲对它抽样时，m(t)将被这些抽样值所完全确定。•Thesamplingrateof2Wsamplespersecond,forasignalbandwidthofWHerz,iscalledtheNyquistrate;itsreciprocal1/2WiscalledtheNyquistinterval.CommunicationSystemsPulseModulation132sfW14第9章模拟信号的数字传输9.2.2带通模拟信号的抽样定理设带通模拟信号的频带限制在fL和fH之间，如图所示。即其频谱最低频率大于fL，最高频率小于fH，信号带宽B=fH－fL。可以证明，此带通模拟信号所需最小抽样频率fs等于式中，B－信号带宽；n－商(fH/B)的整数部分，n=1，2，…；k－商(fH/B)的小数部分，0k1。按照上式画出的fs和fL关系曲线示于下图：fHf0fL-fL-fH)1(2nkBfs15第9章模拟信号的数字传输由于原信号频谱的最低频率fL和最高频率fH之差永远等于信号带宽B，所以当0fLB时，有BfH2B。这时n=1，而上式变成了fs=2B(1+k)。故当k从0变到1时，fs从2B变到4B，即图中左边第一段曲线。当fL＝B时，fH＝2B，这时n=2。故当k＝0时，上式变成了fs=2B，即fs从4B跳回2B。当BfL2B时，有2BfH3B。这时，n=2，上式变成了fs=2B(1+k/2)，故若k从0变到1，则fs从2B变到3B，即图中左边第二段曲线。当fL＝2B时，fH＝3B，这时n=3。当k＝0时，上式又变成了fs=2B，即fs从3B又跳回2B。依此类推。B2B3B4B3BB2B4B5B6BfL0fs16第9章模拟信号的数字传输由上图可见，当fL=0时，fs＝2B，就是低通模拟信号的抽样情况；当fL很大时，fs趋近于2B。fL很大意味着这个信号是一个窄带信号。许多无线电信号，例如在无线电接收机的高频和中频系统中的信号，都是这种窄带信号。所以对于这种信号抽样，无论fH是否为B的整数倍，在理论上，都可以近似地将fs取为略大于2B。图中的曲线表示要求的最小抽样频率fs，但是这并不意味着用任何大于该值的频率抽样都能保证频谱不混叠。CommunicationSystemsPulseModulation17PracticalsamplingIdealsamplingPracticalsamplingNaturalsamplingFlat-topsampling:PAMInpractical,deltafunctioniscloselyapproximatedbyarectangularpulse.Thesmallerthedurationofpulsethebetterwillbetheapproximation.CommunicationSystemsPulseModulation18CommunicationSystemsPulseModulation193.3Pulse-AmplitudeModulationPAMPAMisthesimplestandmostbasicformofanalogpulsemodulation.PAMsignal:)()()(snsnTthnTmts3.10SampleandholdTwooperationsforgenerationofPAMsignal:1.Instantaneoussampling2.LengtheningCommunicationSystemsPulseModulation20otherwiseTt0,tTt0,0,21,1)(thPropertiesofSampleandholdcircuitInstantaneouslysampledversionofm(t)is()()()ssnmtmnTtnT)()()(thtmts)()()(snsnTthnTmts()()()sskSffMfkfHf)(tSTm(t)s(t)h(t)=rect(t/τ)CommunicationSystemsPulseModulation21ComparisonIdealsamplingFlat-topsamplingorPAM()()()3.18sskSffMfkfHfComparedtoidealsampling,wehaveH(f)here.Itproducesdistortion.()()3.2ssmGffGfmfCommunicationSystemsPulseModulation22Apertureeffect(孔径效应)Themagnituderesponseoftheequalizerisgivenby11()sin()sin()fHfTcfTfTThedistortioncausedbytheuseofPAMtotransmitananalogsignalisreferredtoastheapertureeffect.Aperturedistortioncanbecorrectedbyconnectinganequalizer(均衡器)incascadewiththelowpassreconstructionfilter.CommunicationSystemsPulseModulation233.4OtherFormsofPulseModulation1.PulseamplitudemodulationPAM2.Pulse-durationmodulation(Pulse-widthmodulation)PDM3.Pulse-positionmodulationPPMCommunicationSystemsPulseModulation24(a)Modulatingwave.(b)Pulsecarrier.(c)PDMwave.(d)PPMwave.25模拟信号的数字传输模拟脉冲调制波形（a）模拟基带信号(b)PAM信号(c)PDM信号(d)PPM信号UWB定义TimeFrequency-20-100绝对带宽(DARPA)绝对带宽(FCC)中心频率频率轴归一化功率谱（d