Probabilistic Methods of Signal and System Analysis PDF
Preview Probabilistic Methods of Signal and System Analysis
ProbabilMiestthiocdo sf Signaanld S ysteAmn alysis THIRD EDITION R. D. GeorgeC ooperC lareM cGillem ProbabiMleitshtooidfcs SignaanldS ystAenma lysis Third Edition THEO XFORD SERIIENSE LECTRICAANLDC OMPUTEERN GINEERING SERIEESD ITORS AdelS .S edrSae,r iEedsi toEr,l ectrEincgailn eering MichaRe.lL ightnSeerr,i Eedsi toCr,o mputEenrg ineering SERIETSI TLES Alleann dH olberCgM,O S AnaloCgi rcuDiets ign Bobi,:owE,l ementLairyn eaCri rcuAinta lys2insd,E d. .B obrowF,u ndamentoafEl lse ctrEincgailn eer2inndgE ,d . CampbelTlh,eS cienacned E ngineeroifMn igc roelectFraobnriicc ation ChenA,n alogD igitCaoln trSoyls teDme sign & ChenL,i neaSry steTmh eorya ndD esig3nr,d E d. ChenS,y steamn dS ignAanla lys2insd,E d. ComerD,i gitLaolg iacn dS tatMea chinDee sig3nr,d E d. Coopearn dM cGillePmr,o babilMiestthiocdo sfS ignaanld S ystem Anaysli3srd,E d. FrancEol,e ctCriircc uFiutnsd r;imentals FortnPeryi,n cipOlfEe lse ctronAincasl:o gD igital & GranzoDwi,g itTarla nsmisLsiinoens Gurua ndH izirogEllue,c tMraicch ineryT ransforme2rnsdE, d . & Boolaen dB ooleA, M odernS horCto ursIenE ngineering Electromagnetics JoneIsn,t roducttoOi potni cFailb eCro mmunicatSiyosnt ems KreinE,l emenotfPs o werE lectronics Kuo,D igitCaoln trSoyls tem3sr,dE d. LathMio,d ernD igitaanldA naloCgo mmunicatSiyosntse m3sr,dE d. McGilleamn dC oopeCro,n tinuaonudsD iscrete· aSnidSg ynsatle m Anaysli3sr,Ed d. MinerL,i neasn dE lectromagFnieetlifdcos rE ngineers Roberatnsd S edrSaP,I CE2,n dE d. RoulstAonn I,n troducttoti hoePn h ysiocfsS emiconduDcetvoirc es SadikEul,e menotfEs l ectromagn2entdEi dc.s , SantiSntau,b beraunddH, o stetDtiegri,t Caoln trSoyls teDme sig2nn,d E d. SchwarEzl,e ctromagnfeotrEi ncgsi neers Schwarazn dO ldhamE,l ectrEincgailn eerAinn Ign:t roduc2tnidoE nd,. Sedraan dS mithM,i croelectrCoinriccu i4ttshE, d . StefanSia,v anSth,a hiaann,dH ostetDteesri,g onfF eedbaCcokn troSly stems, 3rdE d. VanV alkenbuArngµ,l oFgi ltDeers ign Warner andG rungS,eim iconduDcetvoirc Eel ectronics WoloviAcuht,o matCiocn trSoyls tems YariOvp,t icEalle ctroinniM cosd emC ommunicati5otnhEs d,. CONTENTS , ��� Preface xi 1 Inrtodcutiotno Prboabiilty 1 Engineering AppolfiP craotbiaobnisl ity 1-1 RandomE xperimeanntdEs v ents5 1-2 DefinitioofnP sr obabil7i ty 1-3 1-4 TheR elative-FreAqpupernocayc h8 ElementSaertyT heory1 3 1-5 TheA xiomatic Appr1o9a ch 1-6 7 ConditioPnraolb abil2i2ty 1- Independen2c7e 1-8 CombineEdx perimen2t9s 1-9 BernouTlrliia l3s1 1-10 ApplicatoifoB nesrn oulli Tr3i5a ls 1-11 Problem3s8 Reference5s0 Random Varibales 2 sz 2-1 Concepotfa RandomV ariabl5e2 2-2 DistribuFtuinocnt ion5s4 2-3 DensiFtuyn ction5s7 2-4 MeanV alueasn dM oments6 3 2-5 TheG aussiRaann domV ariabl6e7 2-6 DensiFtuyn ctiRoenlsa tteodG aussia7n7 2- OthePrr obabiDleintsyi Ftuyn ctio8ns7 7 2-8 ConditioPnraolb abiDliisttyr ibuatnidoJn) ensFiutnyc tion9s7 2-9 Examplaensd A pplicatiIo0n 2s CONTENTS vi Problem1s0 9 Reference1s1 9 SeveraRaln dom Variablse 3 120 3-1 TwoR andomV ariabl1e2s 0 3-2 ConditioPnraolb ability-Rev1i2s4it ed 3-3 StatisItnidceaple nden1c3e0 3-4 Correlabteitowne eRna ndomV ariabl1e3s2 3-5 DensiFtuyn ctiooftn h eS umo fT woR andomV ariabl1e3s6 3-6 ProbabiDleintsyi Ftuyn ctioofan F unctioofTn w oR andom Variabl1e4s2 3-7 TheC haracteristic 1F4u8nc tion Problem1s5 2 Reference1s5 8 Elemenst ofS tatistics 4 159 4-1 'Introduc1t5io9n 4-2 SampliTnhge ory-ThSea mplMee an 160 4-3 SampliTnhge ory-ThSea mplVea rianc1e6 6 4-4 SampliDnigs tribuatnidoC nosn fidenIcnet erva1l6s9 4-5 HypotheTseisst ing1 73 4-6 CurvFei tt_ianngdL ineaRre gressi1o7n 7 4-7 Correlatbieotnw eeTnw oS etosf D ata 182 Problem1s8 4 Reference1s8 8 Random Processes 5 189 5-1 Introduct1i8o9n 5-2 Continqoaunsd D iscreRtaen domP rocess1es9 1 5-3 DeterminiasntdN iocn determipRiasntdiocmP rocess1es9 4 5-4 StationaanrdNy o nstatioRnaanrdyo mP rocess1es9 5 5-5 Ergodaincd N onergodRiacn domP rocess1es9 7 5-6 MeasuremeofnP tr ocess Param1e9t9e rs 5-7 SmoothiDnagt awi tah M ovinWgi ndowAv erage2 03 Problem2s0 5 Reference2s0 8 CONTNETS vii CorrelatFiuonntc oins 6 209 Introduct2i0o9n 6-1 ExamplAeu:t ocorrelaFtuinocnt ioofan BinarPyr oces2s1 3 6-2 PropertioefAs u tocorrelaFtuinocnt ion2s1 6 6-3 MeasuremeonfAt u tocorrelFautnicotni on2s2 0 6-4 ExamploefsA utocorrelation F2u2n7c tions 6.;.5 CrosscorreFluantcitoino n2s3 0 6-6 PropertoifCe rso sscorreFluantcitoino n2s3 2 6-7 Exampleasn dA pplicatoifoC nrso sscorreFluantcitoino n2s3 4 6-8 CorrelaMtaitorni cfoers S ampleFdu nction2s4 0 6-9 Problem2s 45 Reference2s 56 7 SpectralD enstyi 2s1 Introduct2i5o7n 7-1 RelatioofSn p ectrDaeln sittoyt heF ouriTerra nsform2 59 7-2 PropertoifSe pse ctrDaeln sit2y 63 7-3 SpectrDaeln siatnyd t heC ompleFxr equenPclya ne2 71 7-4 Mean-SquaVrael uefrso m SpectrDaeln sit2y 74 7-5 RelatioofSn p ectrDaeln sittoyt heA utocorrelFautnicotni o2n8 1 7-6 WhitNeo ise2 87 7-7 Cross-SpeDcetnrsailt 1y 89 7-8 AutocorrelFautnicotniE osnt imaotfSe p ectrDaeln sit2y 92 7-9 PeriodogErsatmi maotfSe p ectrDaeln sit3y 01 7-10 Examplaensd A pplicatoifoS npse ctrDaeln sit3y0 9 7-11 Problem3s1 5 Reference3s2 2 Respo,nes ofL ineaSry stemtso Ra ndom Inputs 8 323 Introduct3i2o3n 8-1 Analysiints h eT imeD omain 324 8-2 Meana ndM ean-SquaVrael uoef S ysteOmu tput3 26 8-3 AutocorrelFautnicotnio ofnS ystem Out3p3u0t 8-4 CrosscorrebleattwieoeInnn puatn dO utput3 35 8-5 ExamploefsT ime-DomaSiyns teAmn alysi3s3 9 8-6 Analysiints h eF requenDcoym ain 345 8-7 SpectrDaeln siattyt heS ysteOmu tput3 46 8-8 CONTENTS viii 8-9 Cross-SpeDcetnrsailtb ieetsw eeInn puatn dO utput3 50 8-10E xamploefsF requency-DoAmnaailny si35s2 8-11N urp.ericCaolm putatoifSo ny steOmu tput35 9 Problem3s6 8 , Reference3s8 0 9 Optmium LineaSry stmes 381 9-1 Introduction 9-2 CriteorfiO ap t38i1m ali·3ty 8 2 9-3 Restricotnit ohneOs p timuSmy stem3 84 9-4 OptimizabtyiP oanr ameAtdejru stme3n8t5 9-5 SysteTmhsa Mta ximiSzieg nal-to-RNaotiiso3e9 5 9-6 SysteTmhsa Mti nimiMzeea n-SquEarrroer 402 Problem4s1 2 Reference4s1 8 Appendiecs A MathemtaiaclT ablse 419 A-1 TrigonomeItdreinct it4i1e9s A-2 IndefinIinttee gra4l2s0 A-3 DefiniItnet egra4l2s1 A-4 FouriTerra nsforOmp eratio4n2s2 A-5 FouriTerra nsform4s23 A-6 One-SidLeadp laTcrea nsform4s23. B FreuqentlEyn ocunetred Prboibtyla iDistbruitinos 425 B-1 DiscrPertoeb abiFluintcyt io4n2s5 B-2 ContinuDoiusst ribut4i2o7n s C BinomliC aoeffiicenst 431 D NormalP rboabiitylD itsrbiutino Function43 2 E TheQ -Funtcion4 34 -; Stude'nst DitsrbiutiFounn tcino 436 t G ComputeCro mputaotnis 438 CONTENTS Ix Tableo fC orretliaoFnu ntcino-Spectral H DensiPtya isr 466 ConoturI ntgertaion46 7 475 Index PREFACE ------------------------ Theg oaoltfsh e ETdhiiatrriedeosn nst eitahslemal ey t ahsoo stfeh e ea reldoiinetvsrzii ,. , tpor oavinin dter otdtouh acept piloioncpf ar toibtoahnbesito ltorih syteuo y tl oipfor no blems asriiintngh a enl ayossfii sg annsadsyl tset mhisaas tp profoprer nigaitnseet euradtitehn negt s jurno isroe nlie.ovH reo lweivmtea aryl, ss eogr rvaed sutautadenee dnn tgsia nasce oenrcsi se revoimfea wt tehraitap lrit eohvueesnylc yo uinwnti edsreceladyts toceuerrse.d Tihesd idtiifffroeonrt msh fi er sste acinosndne d v reercsa.tpIl setn h eidsiu tsoietfo h ne compiust eirnb torittonhed e xuxtca emadpn ildsne e sl percotsbeT.ldh ce eom mpeuxtaemrp les arec arrioeudut s iMnATgL AaBn tdhp er obalrseeum tcshh ta htce aybn eh anwdiltehd thSet uEddeinottMfi AToLn1A aBsw ealswl i otthhc eorm pmuattehrea mpaptilioi.cnc ssa t Iand d.ti toth iieon ntroodcfuo cmtpuiusgotaeines n ro lpvrionbigln evmossltt viaisantngid c s ranpdorocme� os.ts chehearh nagavelesbs eome an.d I epna rtiacn uulmoabfre ,rsn eecwt ions havea dbdeveeidnr, ta ulotalfhl eelxc yei rhsaebvsee me ond ioficreh da nang uemdob,tfe h re probhlaebvmeemse o nd iafinaend du ,m obnfee rpw r obhlaebvmeease d nd ed. Snictiehis as en n ginteetexhtrteri, en agith sme seutnrritaic t hreirg soat,rnht odahsu netu dent wifilnmlda enxy amopfl aetpshp el oitfch acetosineoct neeo np gtisnp ereomrbsHil.one wge ver, iitns oc to mpdleevtooetfilh mdyea thesmuabtetisalc,ncea dotl in siadtetrehanabbtseli eeon n devtopoto eidon utstion omgtfe h dei fficumlatkamie oe arsde v tahsnatctouet fddh ys e uj cbet esnsteiiofan ilets mo a sitTteh.are u tbheolrtishet avheteed ucapotrcieiobssnes ass let rv ed byr epeeaxtpeodsd uirffisecu juctbelmtota ttthetireis;xis t n tetbnoetd heed firstto exposure probaanbrdia lnipdotrocyme asnswdeeh,s o pneot,thl eaT shte. bnoocotok m pirse hensive, budte saellse wcitttihhvto eoslpetyi ht cahasteu thhaovresm ofoususnteid futn lh se o louft ion enginpereomrbsil.ne g brdiiesfc oufs sositfooh msneei gnnfetia fitcouatfrh eiss w ihbleolslo etpkth s et foarg e A ad iscoutfsh vsreai iowonau iyscts ab nue sEelde.m ecnotnacordefyip stpcsrr oebtaaerb ei lity intriond uCc1he:fiad rp frstotetm rh i en tusittainovdfep r oteihlnefrat et qiuvaeepn pcryo ach antdh ent hmfreoo rrmie g sotraonuodsafp x oiiopnmrtao tbiSacbip imlelexi atmiypl.rll aeutsse t altlh ceosen caenapdrmt eos mr ee anitenon ggfuiltn heaaerntre hts er adeixtaimoopnfla els selerceatdniw dnh gib taefrl olumsrn Tsh.ce o nocfaer patn vdaormii isan btlreio nd uced Cha2pa tleowrni tgth hied oepfar so bdaibsitlriibtduyet nifusoniincto tymna esnav,dnau les, ancdo ndpirtoiboanAsba iilgl ninfettia yfit.cou atfrih ecs h aipastne e xrst iedvnies coufs sion MATLABi ts hree gisttreardeedom faT rhke MWaotrshkI, cn .N,a tiMcAk., xi PRAECFE. xii madniyff eprreonbdtae bnifuslniictttayyin t odhpn eyhs s lis ciatuiawnth iitochmnheas yoy c cur. Cha3pe txetrte hnreda snv daormci oanbtclsoeeu ip attt iinovnostl wvomi onorrgrae n dom variaanibdnl tersto hcdeou nccoeesfspt sattltsii i ncdaepaenncddo ernrceel ation. ICnh a4p,st aemrp tlhieanosagr p yp,tl osi tesadtlt ie icsatiimcasot niesoriinesndd,o me detaanatid hl o rdoiusogcnohusf sa smmipelaaenns d ma pvlaer iigasin .vTo ehedne i stribution otfh sea mipdsle es carntidhbu eeso decf o dnefinicnet eirmnva akslitsnsa gtt diiecscaiilo ns ibso ctohne sraienddid ls lturbaymt aenedyx amophfly epsso ittsseht e.iT nhge porfo blem fittsimnogo tht oec xuprevrdeiasmit easannl tayazle d,u soaeflnn ider aetreg hsresi iso n ilslturbaypt readce txiacsmTa.phl lpe er obolfde emt ertmhcieon rirnbegel tawtdeiaeotnna seitessx amiried. Ag endeirsaclou rfsa snipdoroenoms c asnetdsh c eliarts isioigsnfii cvaCehna 5piT.tn he er emhpahseiirsose sn e cltepirnogb maobditelhliasutt sy e iasfunrol el evnignignp ereeomrbsil.n g Accoragd rideneagoatlafl yt ,te idnset vitoototnhp e ehsd yi sciaglnn cietfi hvcoeaiaf rop uorsc ess clacsiasotwinifisnt,oah t taemtma ptth ermiaAgtu oinrci.feaq alut oeutf rih cesh awphtieicrsh, contiisnnu ubesdce hqaupeiatnsinet nr tsr,o tdtouh pcert aicpotrnio cboaelflse tmi tmhaet ing meaoanf rapnredosofrcsmoa mno bsesravmfuepndlc etT ihtoeen c.h onsfim qouoedta htian g wiatm ho vwiinngd doiws ciuss sed. Propaenradtp ipelsio cafau ttioocnoasrnc rdre oolsrasrtceifulonanct tiiodonin ssc uasrsee d iCnh a6p.Mt aenrey x amaprplere ess ieannn at tetdte dome pvtse olmioenpg s hiitnt thoe natucroerr eofulfna ctntisTio.hoin em poprrtoaobneflts e tmi amuattoicnofgru rnecltaitoinosn idsi sciusnso sdmeeedta aniidlsl lt urwaitstveehed cr oamlp euxtaesmr.p l· e Cha7pt tuetrnraos fr equencrye-pdroemosarfeian nnt pdaroteomisc obsnyei snt roducing thceo nocsfep pectdt ernaUslni ltmiyok.tse et xw thsis,cip hmld ye fisnpee dcetynra satsilh t e Foutrriaenros tffoh creom r rfuenlcattamii ooofrnnue, n damenitasad lo hpaetpirepriedr oach ordtbeorr io nutgthp eh yssiicgnanclie fit chcoaeof n cTehcpihtsa. ip tsth meeor ds itf ficult onietn h beo obkut,tha eu tbheolrtishme eav tese hroibuaerll ed s ietnniht wsea dMy e.t hods p oefs titmhsaept eidcnetgnr frsaoiltmt h ayeu tocorrealnfradot tmih poeen r ifoudnogrcatmi on ardee vealnoidpls eltdurw aihtat epdp rocpormipautteeex rpa-lmbTeahsse.eo dwfun i sdeo w fnucttiioom npsre osvteii misal rtlaeuatsswes ted a ltslh ueso etf h ceo mptucota erorru yt inteogtfrh saept eidcoetnnr usasgilbi t onytt hrhee a ancldo mpfrleeqxur eenpcrtyeni ssoe.n ta Cha8pu tteirtl hcieoz necsoe cfpo trsrfu enlcattiisoopnnes dc etaynrnt sadaoil n t atlhyez e rsepoonfls iens seytaertm rosa nidnop.mu tIssne ntiashcs eh ,a patc eurl miiosnfa al tli on thparte cieatdn,ied psd a rtisciugnlnttaieo rfin lcgyai wnhemoeu rsstt huecssoeen . cI etp ts conmtaaniyn se xamplteeosn gtihnpaerteo rabairineneedmpg m hr sae tslhienezvefo eaersnd t mathemmoadtteihlacarsbate ol r t eihas altnmidac n agTehcaeob mJ.lmltea.ot sfsiy tooenum t put thrsoiuumglhai tesix oanma inindle ldu wsitctroham tpeeuxdta emrp les, Cha9pe txetrte hncedo sn coesfpty tesasmn ssa itlcsoyo indssesyrt etmhasaro tep tiimnu m sosmeen Bsohtet hCl.ea i scsmaalt cfithlefoerrkd n oswinga nntadhWl eis e finlefotrrre arn dom siganrael escr ofrenodasm nei ldemsetnatnaCdropymo pieunxttae.mor pof lp etsi mization are conesraienddid ls lturwaitatenehd x amoapfnal dea pfitlitveer . SevAeprpaelna driienuc cdeltespod r ouvsiedmfeau tlh eamnasdtts iatctitaicalbaa llne ds daAtpap.e Gnc doinxatd aeitndasii slcewudihs et sxipaolmonetf,sh a ,ep ploicfco amttepiruosn ttoh aen saiolssfy igannasdlye ssma tsn cdas ne ravasne i ntrotdsouo comttefih woean y s MATLAcBab neu stesodo sluvpcerh o sb.l em
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