第五章研究生现代通信原理-脉冲编码调制理论(PCM)-201

[e-mail]2013-8-322013-8-33PCM†6††APCMTDMPDHSDH2013-8-34PCM††††††††2013-8-35†††2013-8-36(1)A.†,()Hf,0)(txsfHf2(){}snTx)(tx2013-8-37)(tx)(tTδ)(tTδ)(tx)()()(ttxtxTsδ=2013-8-38,[])()(21)(ωδωπωTsXX∗=)(ωX1()()2()()()FTTFTsssnnStnnTδδωπδωδωωωδωω−∞∞=−∞=−∞⎯⎯→←⎯⎯=−=−∑∑2013-8-39)(1)()(1)(∑−=⎥⎦⎤⎢⎣⎡∑−∗=∞+−∞=+∞−∞=nssnsssnXTnXTXωωωωδωω)(ωHHssoTHXXωωωωω⋅=)()()(2013-8-3102013-8-311⎪⎩⎪⎨⎧≤=,0,1)(HHHωωωωω[][]∑∑∞−∞=∞−∞=−−=−∗⎟⎟⎠⎞⎜⎜⎝⎛=∗=nsHsHssnssHHssnTtnTtnTxTnTtnTxttTtxthtx)()(sin)(1)()(sin1)()()(ˆωωδωω2013-8-3122013-8-3132013-8-3142013-8-3152013-8-316B.fHfLB=fH-fL0M1sf⎟⎠⎞⎜⎝⎛+=⎟⎠⎞⎜⎝⎛+−=NMBNMfffLHs121)(2[])()(MLHHLHHLHfffNNfffffB−−−=−=2013-8-317-fH-fLfLfH-fL+kfs-fH+(k+1)fs2013-8-318HLLHHLsHHsHLsLfMNfffMNBMNffkfkfffkffkff)11())(()()11(2)1(2)1(+−=−+=+=+≤+≤≥++−≤+−2013-8-319BNMNNfNMBfMNMNNNffNkNkMNMNkfMNkfkfsHsHHsH112)1(21122111)11)(11()11)(11(2)1(2−−+≤≤++−+−≤≤+=+≥+≥+−++−+≤+≤2013-8-320:1.(fH-fL)2.fH/(fH-fL)N3.M=fH/(fH-fL)-N.4.fS=2(fH-fL)(1+M/N).2013-8-321B2B3B4B5B6BB2B3B4B5B6B2013-8-3221fH=NB(N,Bf(t)2NB2BN=32B2013-8-3232013-8-3242013-8-3252013-8-3262013-8-3272013-8-3282013-8-3292(1/)sfBMN=+2()sNfNBMB=[phone]()()()sTxtxttδ=2013-8-3312013-8-332C.1)()(snnTtptc−∑=∞−∞=)(tp∑−⋅=⋅=∞−∞=nssnTtptxtctxtx)()()()()()(tc∑=∞−∞=ntjnnseCtcω)(2013-8-333∫=−−22)(1sTsTsdtetpTCtjnsnωsωsT∑=∞−∞=ntjnnsseCtxtxω)()(∑−=∞−∞=nsnsnXCX)()(ωωω2013-8-3342013-8-3352013-8-336C.22013-8-3371232013-8-338h(t)()()()()()sTSSnxtxttxnTtnTδδ∞=−∞==−∑()()()()()sfsSSnxtxthtxnThtnT∞=−∞=∗=−∑:⎩⎨⎧≤=0,A,)(τtth2013-8-339[][]∑∑∞−∞=∞−∞=−=−===nssssssfXTATHnXHXXAH22sin)()()()()()(2)2sin()(nωτωτωωτωωωωωωωτωττω2013-8-340——)2sin(2ωτωτ2013-8-341Qx)XY2013-8-3421A.{}L.,1,2,......k,)(1==≤==+kkkyxxxQxQykxkkkxx−=∆+1yxx2013-8-343QLYK(K=1,2,…L),YKXKXK+1YKXKXK+1∆K=XK+1-XK2013-8-344)(xQxyxq−=−=qx)(xpx[][]dxxpxQxxQxExq)()()(222∫−=−=∞∞−σ2013-8-345LL∑∫−==+Lkxxxkqkkdxxpyx1221)()(σ)(xpx{}kx{}Lkyk,......,2,1,=2qσ2013-8-346B...L1,2,3,....k)(210,1,,2=+=⇒=∂∂−optkoptkoptkkqyyxxσ.L1,2,3,....k)()(0,1,1,,,2=∫∫=⇒=∂∂++optkoptkoptkxoptkxxxxoptkkqdxxpdxxxpyyσ2013-8-347L12,,1,optkoptkoptkxxy+≈+kkxkxpP∆≈)(2013-8-34811YYKKXXKK202,3,...,qkkLxσ∂==∂()()221-()-()0kkxkkkxkxyPxxyPx−−=11221[-]()[-]()0kkkkxxkxkxxxkxyPxdxxyPxdxx+−−∂⎡⎤+=⎢⎥⎣⎦∂∫∫2013-8-349(),,1,1,1,12,3,...,2koptkoptkoptoptLoptxyykLxx−+=+==−∞=∞2013-8-35022XXKKYYKK201,2,...,qkkLyσ∂==∂11221[-]()[-]()0kkkkxxkxkxxxkxyPxdxxyPxdxy+−−∂⎡⎤+=⎢⎥⎣⎦∂∫∫2013-8-351()()1,1,,,,koptkkoptkxxxoptkoptxxxoptxpxdxypxdx++=∫∫2013-8-352L1()()1,1,,1,,,,2koptkkoptkxxkxoptkoptkoptkoptxxkxoptpxxdxxxypxdx++++≈=∫∫2013-8-353q(t)=x-Q(x)222-[-()][-()]()qxExQxxQxPxdxσ∞∞==∫C.2013-8-354KPK{}()()()11kkkxkkkxkkpPxxxpxxxpx++=≤=−=∆C.2013-8-355()()()()()1122121331133kkkkLxqkxkxkLxkkxkkLkkkkkkkxypxdxpxydxxyxypσ++==+==−≈−∆⎡⎤−−=−⎢⎥∆⎢⎥⎣⎦∑∫∑∫∑2013-8-356()()()()()3313312311/2/2332424111212LkkkLkkkLLkkxkkkkkkpkkpppx====⎡⎤∆−∆=−⎢⎥∆⎢⎥⎣⎦⎡⎤∆∆=+⎢⎥∆⎢⎥⎣⎦=∆=∆∑∑∑∑2013-8-357†Px(x)†2013-8-358C.∑∑∑∫∑∫==+==∆=⎥⎦⎤⎢⎣⎡−−−∆=−∆≈−=++LkkkLkkkkkkkkxxkkkLkxxxkqPyxyxPdxyxPdxxpyxkkkk121331L121221213)(3)()()()(11σ()kxpkxk∆=P2013-8-359VVk∆V)()(12122±∫∆=−dxxpVVxkqσ∫−=∫∫++−=∞∞−∞−VxVVxxqodxxpVxdxxpVxdxxpVx)()(2)()()()(2222σ2013-8-360222qoqqsσσσ+=2013-8-361(1),LLVk2=∆≡∆2221212231212121LVPPLkkLkkkq=∆=∑∆=∑∆===σ2013-8-3622013-8-3631.Am,22222223)3(2LVALVASmmq⎟⎠⎞⎜⎝⎛==σnL2=⎟⎟⎠⎞⎜⎜⎝⎛=2VADmn2013-8-364dB16dB2223LDSq=σ[]nDDSndBq02.6lg2077.42lg20lg203lg102++≈++=σ[]nSdBq02.676.1max2+=σn2qSσ21=D2013-8-3652.xxxxexpσσ221)(−=xσx2013-8-366D0.2[]DnLDSdBqslg2077.402.631lg10222++≈⎟⎠⎞⎜⎝⎛−≈σ[]DSdBqs1.62≈σ2013-8-3674050dB25dB4050dB25dBn=12[]dBqsS2σ[]dBqsS2σ2013-8-3683“”“”“”2qSσ2013-8-3692013-8-370)(xfz=2013-8-371†††xyx∫∞−=xxdxxpkxf31)]([)(∫∞−=vxdxxpVk31)]([302min2])]([[32][31∫=σVxqdxxpL2013-8-372†††††xBxfln1)(=∫∆=σVxqdxxpxB02222)(6∫=VxdxxpxS02)(22222201212VBLBNS=∆=2013-8-3732013-8-3744††TNxxxx][21Lr=}1,{][21LiyyyyyiTiiii≤≤=rLr2013-8-375jX{}NYYYY,,,21L={}NYYYY,,,21L=()()kjijYXdYXd,,≤iYiY2013-8-376——2013-8-3772013-8-378†PCM†††2013-8-3792013-8-3802013-8-381—2013-8-3821bbfT=2013-8-383„a.A1⎪⎩⎪⎨⎧≤++≤≤+=11,ln1ln110,ln1)(xAAAxAxAAxxf2013-8-38416)(,1=′≤xfAx24dB20lg16=24ITUG.712A87.62013-8-385A†††A=87.6†Vxxi=⎪⎪⎩⎪⎪⎨⎧→≤≤++→≤≤+=)(1ln1ln1)(0ln1)(11xAAxxAAxxfAA2013-8-386µb.10)1ln()1ln()(≤≤++=xxxfµµITUG.71225533.5dBµ2013-8-387††=255)1ln()1ln()(uuxxf++=2013-8-388AAµ2013-8-389†A13†152013-8-390A132013-8-3912013-8-3922PCM††PCMFBC⎪⎩⎪⎨⎧RBCFBCNBC2013-8-393NBCRBCb1b2b3b4b1b2b3b4b1b2b3b415111111111000141110111010011311011101101112110011001010111011101111101010101010111191001100111018100010001100701110000010060110000101015010100100111401000011011030011010000102001001010011100010110000100000011100002013-8-394PCMA.ITUFBCFoldedBinaryCodeFBCenpLLS)1(41222−+=σ2013-8-3953dB()[]()[]()[]222222tqtqtqneEeEeeEσσσ+=+=+=)1(412−=Lpe2nSσ6108.32568−×=→==epLn2013-8-396B.FoldedBinaryCode151111141110131101121100111011101010910018100070000600015001040011301002010110110001112013-8-397PCMM1M2M3M4M5M6M7M82013-8-398AM2M3M4M5M6M7M800000168422100132168422201064321684430111286432168841002561286432161651015122561286432326110102451225612864647111204810