北京邮电大学通信原理课件--第6章-数字信号的频带传输

6.16.1A11/bRMbits=BOOK100MHzcf=AB6.1A12±12()()()()2211sincsinc444bAbbbb4fRfPfTfTfTRδδ⎛⎞=+=⎜⎟⎝⎠+BOOK()()()()()222224sincsinc1616AcAcBbccccbbPffPffPfAARffffAffffRRδδ−++=×⎡⎤⎛⎞⎛⎞−+=++−+−⎡⎤⎢⎥⎜⎟⎜⎟⎣⎦⎝⎠⎝⎠⎣⎦6.2OOK()1cos2cstAftπ=OOKN()20st=0btT≤0/2()nt1/20()()()irtstnt=+1,2i=(1)(2)f1()st2()stc1/Tb(1)(2)()1st()()00cos2cos222bbTTbbccZATATyrtftdtntftdtππ==+=∫∫ Z+Z0()()()()()200000002000cos2cos2cos2cos2cos2cos22cos224bbbbbbbTTccTTccTTccTbcEntftdtntftdtEntntftftdtdtNttftftdtdtNNTftdtσπππδπππ⎡⎤=×⎢⎥⎣⎦π′′′=⎡⎤⎣⎦′′′=−==∫∫∫∫∫∫∫()2~0,ZσN()()20221102|bbATyNTbpypyseNT⎛⎞−⎜⎟⎝⎠−==()2st()()00cos2cos2bbTTccZyrtftdtntftdtππ==∫∫ Z=()()2022202|byNTbpypyseNT−==2/201()st2()stTV()()12pypy=4bTATV=()1200|244114erfcerfc2224bbbbbATATATPesPZPZATATNNT⎛⎞⎛=+=−⎜⎟⎜⎝⎠⎝⎛⎞⎜⎟⎛⎞⎜⎟==⎜⎟⎜⎟⎜⎟⎝⎠×⎜⎟⎝⎠8b⎞⎟⎠()()22101|erfc4428bbbATATATPesPZPZPesN⎛⎞⎛⎞⎛⎞==−==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠|20011erfcerfc2822bbeATEPNN⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠()1st()1,00bLAtstelseT≤≤⎧=⎨⎩()ht()Lht()()()1,10112220jjbeqLLbAeththtsTteelseθθ⎧T≤≤⎪==−=⎨⎪⎩()(){}()2cos20Re0cjftcbLAftththteelseππθT⎧+≤≤==⎨⎩θ()1st()()()1,1,02bjTeqLLAehstdstdθτττττ∞−∞−=−∫∫()21,1002222bbjjTTjjbLbbATAeAesTdAdeEeEeθθjθθθτττ−====∫∫()()()Lcsntntjnt=+()()2220000102242bbNNATNNEHfdfhtdtNEσ∞∞−∞−∞====∫∫=()()()()()()222jjbcbsbbcbsbbcbsbyEenTjnTEnTjnTeEnTjnTθθ−=++=++⎡⎤⎣⎦′′=++3/20()cnt′()snt′22004bbATNNEσ==()()()22bcbsbbcbyEnTjnTEnT′′′=++≈+()()()20221101|2bbyENEbpypyseNEπ−−==()2st()()cbsbynTjnT=+()()2220222220|byyNEbyypypyseeNEσσ−−===1()st2()stTV22bTbEVE==()()()10011|erfcerfc222bbcbbbEEPesPnTENNE⎛⎞⎛⎞′=−==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠()()22000222220|bbbbbEyNENtEEENbyPespydyedyedteNE−−∞∞∞−====∫∫∫00111erfcexpexp422222bbeEEPNN⎛⎞⎛⎞⎛=+−≈⎜⎟⎜⎟⎜⎜⎟⎝⎠⎝⎝⎠0bEN⎞−⎟⎠6.32FSK()()sin2istitπ=1,2i=0btT≤1bTs=()1st()2st(1)bEρ(2)2FSK02N()1st()2st4/20()1201sin22iEitdπ==∫t1,2i=12122bEEE+==()()()()112120012sin2sin40bTbststdtttdtEρπ==∫∫π=()()()()()()101100sin2sin4sin2sin2sin4sin2sin42wZiyrtttdtitttdtntttaZπππππππ=−=−+−=+∫∫∫dt 1112iiai=⎧=⎨−=⎩()2~0,ZσN0()()()()()()()()()()()()()()212011001100110000sin2sin4sin2sin4sin2sin4sin2sin4sin2sin4sin2sin4sin2sin42sin2sin2σππππππππππδπππππ⎡⎤=−⎢⎥⎣⎦⎡⎤t′′′=−−⎢⎥⎣⎦′′=−−⎡⎤⎣⎦′′=−−−=−∫∫∫∫∫∫∫()′′′′′120042Ntdtπ=∫()1st()2sty5/20()()()()2020214102142011yNyNpyeNpyeNππ−−+−⎧⎪=⎪⎪⎨⎪=⎪⎪⎩TV()()12TTpVpV=0TV=()120111211|erfcerfc22242PesPZNσ⎛⎞⎛⎞⎛⎞=−==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠()20111|e2224PesPZPZN⎛⎞⎛⎞⎛⎞==−=⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠1rfc011erfc24bPN⎛⎞=⎜⎟⎜⎟⎝⎠6.46.4A1BBPSK1Mbit/sbR=100MHzcf=AB6.4A()()221sincsincAbbbbbfPfTfTRTR⎛⎞==⎜⎟⎝⎠BBPSK()()()222sincsinc44AcAcbcBbbPffPff2cARfffPfARRf⎡⎤−++⎛⎞⎛−+=×=+⎞⎢⎥⎜⎟⎜⎝⎠⎝⎟⎠⎣⎦6/206.5BPSK()()1cos2cstAftπ=()(21stst=−)0btT≤()1st()2st(1)bEρ(2)BPSKN0/222bbATE=()()()21212100111bbTTbbststdtstdtEEρ==−∫∫=−()cos2iistaAftcπ=111iiai2=⎧=⎨−=⎩()()()()200022cos22cos2cos2bbbTTTcicwcZibyrtftdtaftdtntftdtAAaTZππ==+=+∫∫∫π Z0()()()()()()()()()()()2222020020002002002204cos24cos2cos24cos2cos24cos2cos222cos2bbbbbbbbTwcTTwcwcTTwwccTTccTbcEntftdtAEntftntftdtAEntntftftdtdtANttftftdtdtANNTftdtAAσπππππδπππ⎡⎤=⎢⎥⎣⎦⎡⎤dt′′′=⎢⎥⎣⎦′′=⎡⎤⎣⎦′′′=−==∫∫∫∫∫∫∫∫′7/20()1st()2sty()()()()22022021022022bbbbAyTNTbAyTNTbApyeNTApyeNTππ−−+−⎧⎪=⎪⎪⎨⎪=⎪⎪⎩TV()()12TTpVpV=0TV=()()21200111|erfcerfcerfc22222bbbTATPesPZTNNσ⎛⎞⎛⎞⎛⎞=−===⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠bE()()()21||bPesPZTPes==20011erfcerfc222bbbATEPNN⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠6.66.6BPSKBPFBPSKθLPFBPFBPSK6.6()cos2cftπθ+cos2cftπBPFBPSK{}2RecjftjAeeπθ±ABPSK10±BPF()nt()(){}2Recjftntnteπ=()()(csntntjnt=+)()nt()cnt()snt0BBPF20NBσ=0NBPF()()(){}2RecjftjcsrtAentjnteπθ⎡⎤=±++⎣⎦cos2cftπ(){}()(){}()ReRecosjcscrtAentjntAntθθ=±++=±+yAξ=±+ξ()cnt()0~0,NBξNA+8/20()22201cos1coscoserfcerfc2222AAPANBθθξθσ⎛⎞⎛⎞−==⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠A−()2201coscoserfc22APANBθξθ⎛⎞=⎜⎟⎜⎟⎝⎠2201coserfc22bAPNBθ⎛⎞=⎜⎟⎜⎟⎝⎠6.7bRBPSK()()()cos2nbcnstagtnTftπθ∞=−∞=−+∑Tb=1/Rb{}1,1na∈+−1cbfT()00bAtgtelseT≤⎧=⎨⎩{}naθ(1)()st(2)BPSK:(1)()st()()nbnbtagtnT∞=−∞=−∑()cos2cftπθ+DSB()bt()()()222221sincsincsincbbbbbbbAfPfATfTATfTTR⎛⎞===⎜⎟⎝⎠bR()st()()()222sincsinc44bcbcccsbbbPffPfffffAPfRRRf⎡⎤−++⎛⎞⎛−+==+⎞⎢⎥⎜⎟⎜⎝⎠⎝⎟⎠⎣⎦(2)9/20()()()cos2nbcnstagtnTftπθ∞=−∞=−∑+)()()()()(()()()()()()2222222cos2cos21cos421cos4cos4222nbccnbnncnmbbmncnbcnvtagtnTftftagtnTftaagtmTgtnTftAAagtnTftπθπθπθπθπθ∞∞=−∞=−∞∞∞=−∞=−∞∞=−∞⎛⎞⎛=−+=+−⎜⎟⎜⎝⎠⎝++2=−−++2=−=+∑∑∑∑∑⎞⎟⎠+2()vt2cfVCO()sin42cftπθ−+2()sin2cftπθ−+()sin2cftπθ+()cos2cftπθ+()cos2cftπθ−+VCO()sin2cftπθϕ−++Qsinnaϕ−Icosnaϕsin2ϕ−ϕ00ϕVCOϕ0ϕVCOϕϕ0()cos2cftπθ+ϕπ=6.8BPSKN0/2=10−10W/HzEb=A2Tb/2AbT310bP−=bR10kbit/s100kbit/s1Mbit/sBPSK10/20A301erfc102bEN−⎛⎞⎜⎟=⎜⎟⎝⎠010lg6.8dBbEN=BPSK01erfc2bbEPN⎛⎞=⎜⎟⎜⎟⎝⎠310bP−=0.68010bEN=20.6810102102bAT−=××9.324.66410210bbARR−−=×=×10Kbps100Kbps1MbpsA0.00440.01380.04386.9DPSKbR110100010110112DPSK3DPSKDPSK04DPSK5DPSK(1)1101000101101011000011011(2)DPSK(3)0000000ππππππ(4)DPSKBPSK(5)DPSK11/206.103Mbit/s2GMHz20001MHz70MHz2MHzB=Rb=3Mbps1.5bps/HzbRB=M21Baud/Hzlogbps/HzM=2log1.5M≥1.52M≥4M=1.5MBaud2bsRR==α()1sBRα=+21111.53sBRα=−=−=12/206.11(34.368Mbit/s)6GHz25.776MHzQPSK17.184MBaud2bsRR==NyquistsRα()1sBRα=+25.7761117.184sBRα=−=−=0.5fc=6GHz6.12OQPSK2MbpsbR=(1)OQPSK(2)11100100OQPSK()It()Qt(3)OQPSK:(1)13/20(2)I1100Q1010()It()Qt(3)OQPS