第3章 随机信号分析.pdf

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1、1?3?3.1?3.2?3.3?3.4?3.5?3.6?3.7?3.8?3-1?x2(t)xn(t)ttt?S1S2Sn(t)tkx1(t)3.1?3.1.1?),(),(1111111txfxtxF=11111)(),(xtPtxF=);,();,(21212212,12122t txxfxxttxxF=221121212)(,)(),;,(xtxtPttxxF=3.1.2?).,;.,(.).,.;,(2121212,121nnnnnnntttxxxfxxxtttxxF=),;,(2121nnntttxxxFLLnnxtxtxtP=)(,)(,)(2211L3.2?3.2.1?111111

2、),()(dxtxfxtE=dxtxfxtEta),()()(1=?3.2.2?=)(tD2)()(tatE)()()(2)(22tatatEtE+=)(),(212tadxtxfx?3.2.3?)()(),(2121ttEttR=?212121221),;,(dxdxttxxfxx=)()(22tatE=)()()()(),(221121tattatEttB=?21212122211),;,()()(dxdxttxxftaxtax=?:)()(),(),(212121tatattRttB=?),(),(2121ttRttB=2?)()(),(2121ttEttR=)()()()(),(221

3、121tattatEttB=?:)()(),(),(212121tatattRttB=)()(),(+=+ttEttR?3.2.4?);();(),;,(22111121212txftxfttxxf=0),(21=ttR0),(21=ttB?3.3?3.3.1?),;,(),;,(21212121+=nnnnnntttxxxftttxxxfLLLL?1?t?)();(11111xftxf=?2?);,(),;,(21221212xxfttxxf=?3?)(tEdxtxfx);(1=a=dxxfx)(1=?4?2121221);,(dxdxxxfxx=)()(),(2121ttEttR=)(R=

4、)(tD=)(),(212tadxtxfx2=?)(tEa=)(tD2=),(21ttR)(R=?3.3.2?a=2/2/)(1limTTTdttxT)(tx=)(R)()(+=txtx+=2/2/)()(1limTTTdttxtxT?1?aa=)()(RR=?_/2222/21()lim()TTTx tax ta dtT=22=3?3.3.3?)()()(+=ttER?1?)()0(2tER=)(t?)()(=RR?2?1.?)0()(RR?3?4?)()(2tER=)(limR)()(lim+=ttE)()(+=tEtE)(2tE=)(t?5?2)()0(=RR)()()(22tatEtD

5、=)(t?)(R)0(R)(R202.?f(t)Otf T(t)tOT2?T2TFPTTf2)()(lim=TFEPEPTTf2)()()(lim=?dTFEdPSTT2)(21)(21lim=?-?)()(PR)()(fPR?3.?deRfPfj=2)()(dfefPRfj=2)()(deRPj=)()(dePRj=)(21)(?4?1?0)(P?2?)()(=PP?3?dffPR=)()0(?4?3-1:?A?(0,2?)?1?2?3?)cos()(+=tAtcc)(t)(t)(tdtAtEtac21)cos()()(20+=dttAcc)sinsincos(cos220=sinsinco

6、scos22020dtdtAcc=?1?)(t?:?:)(t?(0=)()(),(2121ttEttR=?)(t)cos()cos(21+=tAtAEcc2)(cos)(cos212122+=ttttEAcc+=20122122212)(cos2)(cos2dttAttAcc0)(cos2122+=ttAccAcos22=?)(t)()(2)(2ccAP+=?2?)(t2)0(2ARS=?3?0)cos(12/2/lim=+=dttATaTTcTdttAtATRcTTcT)(cos)cos(1)(2/2/lim+=)22cos(cos2lim2/2/2/2/2dttdtTAcTTcTTcT+=

7、cAcos22=aa=)()(RR=?)(t3.3.4?1?2?=nnnTtgat)()(?)(tg?na5?1?)(t=nnnnnTtgaEnTtgaEtE)()()()()()nnE ag tnT=?)(tE?2?)(t)()(),(+=+ttEttR=+=nmmnmTtgnTtgaaE)()()(=+=nmamTtgnTtgnmR)()()(?)(t3.4?3.4.1?3?)(tdettRPj+=),()()2)(exp(21)(22axxf=f(x)12Oax?)2exp(21)(2xxf=21212.)2(1Bnn=)(21exp11kkkjjjnkjknjaxaxBB=22)(kk

8、katE=),;,(2121nnntttxxxfLL11121221112LMOMMLLnnnnbbbbbbB=kjkkjjjkatatEb=)()(|B|jk?|B|?bjk?0)()()()(),(212121=aatEtEaattEttB)(t?)(t?3.4.2?1?n?n?2?3?=njjjjnjjnax122122)(exp)2(12)(exp21221jjjnjjax=),;,(2121nnntttxxxfLL21212.)2(1Bnn=)(21exp11kkkjjjnkjknjaxaxBB=),(),(),(2211nntxftxftxfL=11121221112LMOMMLL

9、nnnnbbbbbbB=?4?2)2exp(21),(2222yxyxf+=3.4.3?Q?21()exp()22xQdx=?=xtdtexerf022)(?dtexerfxerfcxt=22)(1)(6?fcOS(f)fffcf(a)tOS(f)?a(t)?fc(b)3.5?3.5.1?)(cos)()(tttatc+=0)(tatttttcsccsin)(cos)()(=)(cos)()(ttatc=)(sin)()(ttats=?)(tc)(ts?)(t2?3.5.2?)(tc)(ts?)(ta)(t?3.5.3?)(tc)(tsttEttEtEcsccsin)(cos)()(=0=?0

10、)()(=tEtEsc?ct2=1sin=tc0cos=tccccsin)2(cos=+ccccos)2(sin=+?)()(),(+=+ttEttRsin)(cos)(ttttEcscc=)(coscos),(+=ttttRccc)(sincos),(+ttttRcccs)(cossin),(+ttttRccsc)(sinsin),(+ttttRccs)(sin)()(cos)(+ttttcscc)(R=0=tctcsctcttRttRRsin|),(cos|),()(00=+=?t?)(),(ccRttR=+)(),(cscsRttR=+ccsccRRRsin)(cos)()(=ct2=c

11、sccsRRRsin)(cos)()(+=?)()(scRR=)()(sccsRR=)()(=sccsRR?)()(=cscsRR0)0(=csR?0)0(=scR)0()0()0(scRRR=222sc=701=tttttttcsccsin)(cos)()(=)()(11ttc=ctt22=)()(22tts=?)(tc)(ts)(tcs3.5.4?)(ta)(t?),(scf),(af?)(af)(f?sc,?2exp21)()(),(2222scscscfff+=2)(exp21)(22axxf=?),(),(),(),(afafscsc=scscscaaf),()(cos)()(tta

12、tc=)(sin)()(ttats=cosac=sinas=cossinsincos),(),(aafafsc=),(scfa=2)sin()cos(exp2),(2222aaaaf+=2exp2222aa=dafaf),()(=0,2exp222=aaadaa2exp220222=?daaff),()(0=)2exp(212202daaa=2021=?2)(t)(ta)(t)(ta)(t)()(),(fafaf=3.5.4?tttttcsccsin)(cos)()(=)()(scRR=)()(scPP=()()220ccWWPP?+?=?)(ttccostcsin?)(21tc)(21tst

13、ttttttccsccccossin)(cos)(cos)(2=tttttcsccc2sin)(212cos)(21)(21+=tttttttcscccc2sin)(cossin)(sin)(=tttttcsscc2cos)(21)(212sin)(21+=8ttfccos)()()(21ccFF+ttfccos)()()()(21ccF+ttccos)(21)(P2costjtjccceet+=4tjtjccee+tccos?+)(41)(412ccttccos)()(41)(41ccPP+)(Pcc0WW)(cPc202W2W)(cP+c02W2W02W2W)(0P?)(sP)()cos(

14、)(tntAtrc+=ttnttntncsccsin)(cos)()(=ttnAttnAtrcsccsin)(sincos)(cos)(+=0),()(21exp)(202222+=zAzIAzzzfnnnttzttzcsccsin)(cos)(=)(cos)(tttzc+=?Rice?3.6?3.7?dthvthtvtvii)()()()()(0=)(tvi)(tvo)(iV)(oV)(th)(H?dthvtvti)()()(0=?dtvhtvi)()()(00=dtvhi)()(=)()()(HVVio=3.7.1?)(ti)(to)(th)(H)(iP)(0Pdthti)()()(00=

15、1.?)(0t)()(0dthEi=)(0tEdtEhi)()(0=0)(dha=dtethHtj)()()0(Ha=?92.?)(0t)()(),(000+=+ttEttR)()()()(00dthdthEii+=ddttEhhii)()()()(00+=ddRhhi)()()(00+=)(oR=?)()()(=hhRi3.?)(0tdeRPj=)()(00deddRhhji+=)()()(00?+=?=deRdehdeahPjijjo)()()()(00)()()()()()(2*iioPHPHHP=4.?)(0tdthti)()()(00=kkkkihttk=)()(lim)(000?5

16、.?)()(),(00+=+ttEttRii)()()(0dthtEii+=dttEhii)()()(0+=dRhi)()(0=)()(hRi=)(0iR=)()()(0=hRRii)()()(0HPPii=)()()(0=HPPii3.7.2?)(titccos)(to?1?2?=ttEttEtEcicicos)(cos)()(0?)()(),(+=+ttEttRooo)(cos)(cos)(+=ttttEcici)()(),(+=+ttEttRooodettRPjoo+=),()()(coscos)()(+=ttttEccii)2cos()cos(21cccitR+=)()(41cciiPP+=103.8?3.8.1?f)(fPn20n00)(R)2(0n)/()(2)(0HzWfnfPn+=bbbTTTR0/1)(?2?2()(bbfTSaTP=bTbT1)(R)(t11tt)(t2/bT2/bT11bTbbbbTTTTttER+=121)1(211)()()(?)(R?=bbbTTTR0/1)(?