北京邮电大学通信原理课件--第5章-数字信号的基带传输

5.1240022log2400log87200bpsbsRRM==×=5.211100101(1)1(2)(1)101000110(2)5.3013()1st()2st01bT1(a)()1st()()21stst=−2(b)()1st()20st=3(1)PAM()()nbnstagtnT∞=−∞=−∑{}na1±[]0anmEa==221aEaσ⎡⎤==⎣⎦()()1gtst=1/28()()sincbbGfTfT=()st()()(222sinca)sbbbPfGfTfTTσ==2()()nbnstagtnT∞=−∞=−∑{}na()0,1()()1gtst=()sinc22bbTTGff⎛⎞=⎜⎟⎝⎠1122nnab=+nb1±()()()1122nbnnstbgtnTgtnT∞∞=−∞=−∞=−+−∑∑b()(12nnutbgtnT∞=−∞=−∑)b()()22sinc4162bbubGfTTPffT⎛⎞==⎜⎟⎝⎠()(12bnvtgtnT∞=−∞=−∑)()()212bmjtTbmnmvtgtnTceπ∞∞=−∞=−∞=−=∑∑()()2222221112211,3,2sin21102440other2bbbbbbmmjtjtTTTTmbTTnbbbbbbbbcgtnTedtgteTTmTmmTmGmTTTmmTπππππ∞−−−−=−∞=−=⎧±=±±⎪⎛⎞×⎪⎜⎟⎛⎞⎪⎝⎠====⎨⎜⎟⎛⎞⎝⎠⎪×⎜⎟⎪⎝⎠⎪⎩∑∫∫dt2/28()(12bnvtgtnT∞=−∞=−∑)()()()222111216421vnnkbbnkPfcfffTTkδδδπ∞∞=−∞=−∞⎛⎞⎛−=−=+−⎜⎟⎜−⎝⎠⎝∑∑1⎞⎟⎠()st()()()2221112sinc16216421bbskbTTkPffffTkδδπ∞=−∞⎛⎞−⎛⎞=++−⎜⎟⎜⎟⎝⎠−⎝⎠∑1(5.2.12)()()()21saTbPfPfGfT=()aPf()aRmDFT{()TGf()Tgt}na5.2.14()()22aaaRmmmσδ=+[]anmEa=()222a2anaaEamEamσ⎡⎤⎡⎤=−=−⎣⎦⎣⎦()mδDiracdeltafunction{}2am1mbbmfTTδ⎛⎞−⎜⎟⎝⎠∑()mδ1(5.2.18)()22aaambbmmPffTTσδ⎛⎞=+−⎜⎟⎝⎠∑(1){}na{}1±0am=21aσ=()1aPf=()()sincTbGfTfT=b()()()()221sincsaTbbPfPfGfTfTT==b(2){}na{}0,112am=214aσ=()1144ambbmPffTTδ⎛⎞=+−⎜⎟⎝⎠∑()sinc22bTTTGff⎛⎞=⎜⎝⎠b⎟3/28()()()()222222221111sinc4421sincsinc1622135sinc21616436100saTbbbmbbbbbmbbbbbbPfPfGfTTfTmfTTTfTmmTfTfTfffTTTTfδδδδδδπππ2=⎡⎤⎛⎞⎛⎞=+−×⎢⎥⎜⎟⎜⎟⎝⎠⎝⎠⎣⎦⎧⎫⎛⎞⎪⎪⎛⎞⎛⎞=+−⎨⎬⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎪⎪⎝⎠⎩⎭⎛⎞⎛⎞⎛⎞⎛⎞±±±⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎝⎠=++++∑∑5.410PAM()()nbnstagtnT∞=−∞=−∑{}na1±[]0anmEa==221aEaσ⎡⎤==⎣⎦()gt()2244sincsinc2222sinsinc22bbTTjfjfbbbbbbbATTATTGffefefTfTjATπππ−⎛⎞⎛⎞=−+⎜⎟⎜⎟⎝⎠⎝⎠⎛⎞=−⎜⎟⎝⎠()()22222sinsinc22absbbbfTfPfGfATTσπ⎛⎞⎛==⎜⎟⎜⎝⎠⎝T⎞⎟⎠0-11-1{}na{}1na∈±{}kb{}1kb∈±{}nanna{}kb22,nnbb1+()()ksstbgtkT∞−∞=−∑4/282bsTT=()00sAtgtelse≤⎧=⎨⎩T221nnnnbaba+=⎧⎨=−⎩()()()()()(isevenisodd22kskkskskkkknsnsnnstbgtkTbgtkTbgtkTagtnTagtnTT∞=−∞∞∞=−∞=−∞∞∞=−∞=−∞=−=−+−=−−−∑∑∑∑∑)s−()()2nsnutagtnT∞=−∞=−∑()()()sstututT=−−()()()()()222214sin2ssssjfTsujfTjfTjfTubuPfPfePfeeefTPfπππππ−=−=−⎛⎞=⎜⎟⎝⎠()ut112sbTT=RZ()()2221sinc42bbubATfTPfGfT⎛⎞==⎜⎟⎝⎠()222sincsin22bbsbfTfPfATπ⎛⎞⎛=⎜⎟⎜⎝⎠⎝T⎞⎟⎠0-11-1{}na{}1na∈±{}kb{}1kb∈±{}nanna{}kb22,nnbb1+()()ksstbgtkT∞−∞=−∑2bsTT=()00sAtgtelse≤⎧=⎨⎩T221nnnnbaba+=⎧⎨=−⎩{}kb()[],biimRiimEbb++=5/28i2in=()[]2102,2110bnnmmRnnmEabmelse+=⎧⎪+==−=⎨⎪⎩i2in1=+()[]211021,2110bnnmmRnnmEabmelse++1=⎧⎪+++=−=−=−⎨⎪⎩{}kb2()()()12,221,212101120bbbRmRnnmRnnmmmelse=++++⎡⎤⎣⎦=⎧⎪⎪=−=±⎨⎪⎪⎩+()()22111221cos2sin2sbbjfmTbbmjfTjfTbbPfRmeeefTfTπππππ∞−=−∞−==−−=−⎛⎞=⎜⎟⎝⎠∑()()()222222112sinsinc222sinsinc22sbsbbbbbbbPfPfGfTfTATfTTfTfTATππ=⎛⎞⎛⎞=××⎜⎟⎜⎟⎝⎠⎝⎠⎛⎞⎛⎞=⎜⎟⎜⎟⎝⎠⎝⎠25.5100000000111001000010AMIHDB3Manchester(1)(2)(3)(1)AMIHDB3Manchester(2)6/28(3)AMIHDB3RZRZMacnshesterRZ5.610()100bAtstelseT≤≤⎧=⎨⎩10()20st=02NBB()nt()ist67/281()1st()yty[]1|Eys[]1|Dysy()()11|pypys=2()2st()yty[]2|Eys[]2|Dysy()()22|pypys=3()1py()2py4TV510btT≤≤()()ytAtξ=+()tξ()nt()tξ0A20NBσ=y0NB()()202101yANBpyeNBπ−−=220btT≤≤()()yttξ=()tξ()nt0020NBσ=y0NB()202201yNBpyeNBπ−=234TV()()12|PsyPsy=|)()()(()||iiipysPsPsypy=TV()()()()1122PspyPspy=10TV()()12pypy=()1py()2py2TAV=5()()()()()()112211|||2bPPsPesPsPesPesPes=+=+2|⎡⎤⎣⎦8/28()()11200||22121erfcerfc2282TAAPesPyVsPAPAANBNBξξ⎛⎞⎛==+=−⎜⎟⎜⎝⎠⎝⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎞⎟⎠()()22201||erfc2228TAAPesPyVsPPANBξξ⎛⎞⎛⎞⎛⎞===−=⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠201erfc28bAPNB⎛⎞∴=⎜⎟⎜⎟⎝⎠5.77()1st()2st()wnt02N71()ht2y()1st3()2sty()2py4(1)()(1()bhtsTtst=−=)22y()()()()2122bbsThdssdATEττττττ∞∞−∞−∞−==∫∫=21bEEE==2bE9/28()()22200222bNNHfdfSfdfσ∞∞−∞−∞==∫∫02NE=(3)y()()()()2212bbsThdssdATEττττττ∞∞−∞−∞−==−=−∫∫byEξ=−+ξ002bNE()2sty2bEA−=−bT02bNE()()20201bbyENEbpyeNEπ+−=(4)y()1st()()()2011|101|bbyENEysbpypyseNEπ−−==TV()()12pypy=0TV=()()()()()()112211|||2bPPsPesPsPesPesPes=+=+2|⎡⎤⎣⎦()()()()()11|0|0bbPesPysPEPEPEξξξ==+=−=b()()()()22|0|0bbPesPysPEPEξξ==−+=()2011erfcerfc222bbbEEPENξσ⎛⎞⎛⎞==⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠01erfc2bbEPN⎛⎞∴=⎜⎟⎜⎟⎝⎠5.8H(f)8f1=1MHzf23MHz812sfff=+()1snHfnf∞=−∞−=∑sf()snHfnf∞=−∞−∑10/28124MbaudsRff=+=24Baud/Hz3sRf=5.99()Hf2000()Hf9a2000(2000nHfn∞=−∞−∑)bα0.5()115002sRα+=21500200010.5sR×==+200011/28c20005.10α11200BaudsR=()11200Hz2sRBα=+=1Baud/Hz=4bit/s/HzsRB=2log4800bit/sbsRRM==5.1116MPAM()Hf1α=11114Mb/sbR={}nb1±16PAM{}1,3,5,,15±±±±1()gtsT(1)AsR(2)B(3)()2Hf(1)21MBaudlog16bsRR=={}nb{}ma[]0mEa=2221315858mEa+++⎡⎤=⎣⎦=()gt()(sinc)ssGfTfT=A12/28()()()22285sincmAssEaPfGfTfTT⎡⎤⎣⎦==s(2)B()()BmBmstagtmT∞=−∞=−∑s()Bgt()()rcosBGfHf=()()2rcos11coscos220esssslsesTffTTfHfTππ⎧⎛⎞T+=≤⎪⎜⎟=⎝⎠⎨⎪⎩B()()222185cos200smABsfTEafPfGfTT⎧⎛⎞⎡⎤s≤⎪⎜⎟⎣⎦==⎝⎠⎨⎪⎩(3)()()HfGf()()sincssGfTfT=()()22sincsKHffT=K5.12myani=++n0a1±2σ3mimi11,0,22−111,,424013/28()()()()()()|11|1|1|12ePPeaPaPeaPaPeaPea1==+=++=−=−=++=−=()()()()()222222|11011131022211211132erfcerfcerfc848222111113erfcerfcerfc848828mmmmPeaPniPniPnPiPnPiPnPiσσσσσσ==++=−−⎛⎞⎛⎞⎛⎞⎛=−=−+−=+−=⎜⎟⎜⎟⎜⎟⎜⎝⎠⎝⎠⎝⎠⎝⎛⎞⎛⎞⎛⎞=++⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎛⎞⎛⎞⎛⎞=++⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠12m⎞⎟⎠()()()()()222222|11011131022211211132erfcerfcerfc848222111113erfcerfcerfc848828mmmmPeaPniPniPnPiPnPiPnPiσσσσσσ=−=++=−−⎛⎞⎛⎞⎛⎞⎛==+=+=⎜⎟⎜⎟⎜⎟⎜⎝⎠⎝⎠⎝⎠⎝⎛⎞⎛⎞⎛⎞=++⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎛⎞⎛⎞⎛⎞=++⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠12m⎞⎟⎠22111113erfcerfcerfc84882ePσσ⎛⎞⎛⎞⎛⎞=++⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠28σ5.13D/A8PAM9600bit/sbR=0.5α=sR133200Baud3bsRR==()12400Hz2sRWα=+=96004bits/s/Hz2400bRW==5.1