Example: Two Stochastic Process u~u[0,1]

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1 Co o Slo o Coco S Sh EE I Gholo ll Sochc Slo Dc Slo l h PLL c Mo o coco w h o c o Ic o Co B P o Go E A o o Po o Th h h o q o ol o oc o lco q ccc lco l Bc El: Uo Dbo Ucol Sl Ab bo col l G col G col Ab bo col l M o Dc Ul o ll lo: Scl A Ebl A Sl h w o wo h lo o b oc. Eoc Sl So wll Pc l co o Slo l co o o 55 Co o Slo o Coco S Sh EE I Gholo ll Sochc Slo El: Two Sochc Poc ~U ξ ~ U ; ξ co ϕ 3 o : b o o b o b o MATLAB co T o Ebl A So Z Ccloo ξ ϕ ξ I Slo w So Sl o S BE oh ; ξ co 56 Co o Slo o Coco S Sh EE I Gholo ll o b Go b Tho Bco Mol Ahc Cl ch G Coc lo : o q ll Coc Bc Co wh A B C D b ± ± b b b b b b > b b b Ll Tho o - o c q 57 Co o Slo o Coco S Sh EE I Gholo ll o b Go L Coc Sqc Go LCG c c > c < : ll c: c : S : ol El: LCG777 ~ o o b oc. Po Lh o b lo obl Po Lh co b h : ll Po I c ll o wll b - Sch o M Po LCG h lh b o l wo > L All c c b LCG Poo: c b > b b A A b c 58

2 Co o Slo o Coco S Sh EE I Gholo ll o b Go L Coc Sqc Go T A: c M Coc Aloh ollco M Tho LCG c h o o : co o c b o 3 b L > > Poo: > q q q q 59 Co o Slo o Coco S Sh EE I Gholo ll o b Go L Coc Sqc Go L 3 I... Lh o LCG c h l coo ll o lh o LCG c o... Poo: B co w o o h ollow c: o : LCG : LCG : LCG Lw D : o o S o o c o c o o c o lh lc LCM o h L3 lh lh 6 Co o Slo o Coco S Sh EE I Gholo ll o b Go So w o o h ho wh ow o b bc... lc Wll b ol... ho l. L > Po ll l o o w c lh wll o ch o L : I c o ll o col b o o ll Bc: Whch obl c b > q c q q q 6 Co o Slo o Coco S Sh EE I Gholo ll o b Go L < < ll h Wh > Th Wh Poo: c coo A > : B o ll ho Th coco. I 3 bc P P P So 9 b L 3 Coc q: 3 q 3 8 q > 6

3 Co o Slo o Coco S Sh EE I Gholo ll o b Go L Poo : Sc Coo B L o ll > : I cl o LCG o ll o o So > Th col h oo o A M ho 63 Co o Slo o Coco S Sh EE I Gholo ll o b Go El: D ll Po T A LCG o E ll > E o c > 3 5 L 5 E ol > 3 E > Th o. 5 ~ 8... E ll > c E o c > E ol > T C7_LCGo. E > 5 Th o. T B: c Mllc wh P Mol llco ol LCG > M Tho LCG h o o - * * l o oo o oo o 7 6 Co o Slo o Coco S Sh EE I Gholo ll o b Go El: 7 h M P cl o~ b Sco L P b o A oo L h: oo o b o ll 6 b o 8 b MPUDSP o l Alco T C: c Mllc wh o-p Mol llco ol LCG > M Tho o o o c LCG h ll o o - 3 o 5 o 8 o Cooll c o ~ olow o b o Two o o b ol o c b oh l l... P 65 Co o Slo o Coco S Sh EE I Gholo ll o b Go Oh Mho: Qc Coc Go b c > El : l ll o co o ll o > bocc Coc Go G c b l B o l. > > 3 o 3 I Coc Go c > : o {... } lw ollow b 66 boh

4 Co o Slo o Coco S Sh EE I Gholo ll o T o T Lo Po c o oh o: I l A l Dl-Col Wh Sl Alco o oh c Ch Sq T Co h occc o ch bol o o co: Ec b o co occc l: P C P P b l oh P >> C h Ch q bo wh - o o I l l co b oo ll o oo b ll h P C ν 67 Co o Slo o Coco S Sh EE I Gholo ll o T Sc Plo Plo o o ll cobo o h o bc El: Two ll Po LCG 65 9 o 8 o 8 68 Co o Slo o Coco S Sh EE I Gholo ll o T 3 Db-Wo Ic T Db Wo P o D A Eoc - l D D: l: E Z colo coc o D D El: Th l o D.995 ho Z col Th l o D.637 ho Co o Slo o Coco S Sh EE I Gholo ll o T Kolooo-So KST Co o q h o l l o b o co co o Ch q P... o Ob Sl.. So h < < Clcl: o o o low K K b b : 7

5 Co o Slo o Coco S Sh o T 5 Scl T h o owl o Coc l. { U { U... U... < } < } : Tl o b co o ll o ccc how l : l c lo Accc -o Co o Slo o Coco S Sh o b Go Kh Mol h. Ql - Sbl cl b. Th hol b cl lo o bo o occ.. Ecc -Th o hol b qc o. Ml o b q. EE I Gholo ll o l o qc ll o h ccc wll b h o oc o w h ol o b ccc Co o b l c l o o c o lo b Scl b o o ll 6 Th oc o o LCG. o Kh ol 6 Oh Scl T T G Kh ol Dh b o o : CD-OM G. Ml EE I Gholo ll 3. bl -Th ho hol b bl o llow o b oc.. Pobl - I h ho l o hol oc h l. 5. Slc -Th o hol b how boh o l o. 7 Co o Slo o Coco S Sh EE I Gholo ll o b Go M S Dcl o oo LCG S o oc oo o M S Aloh: ll Po P ll lcbl 3 El obl o ch Lw Goo Mll M S M P wl o 3 b co 687 o U Ol MATLAB 3-7 h ow MATLAB lo o o o b IEEE lo o 5b o M obl 73 Co o Slo o Coco S Sh EE I Gholo ll o b Go Wch ll Aloh Cob o LCG o c o A Po c c bco c. El: 3 ll o LCG o ql o LCG wh h o o ol 7. T El o o Co o b 333 o 7

6 Co o Slo o Coco S Sh EE I Gholo ll o b Go MATLAB o Go B o Go Ml Sbc wh Boow Aloh G lo o b cl: A co o 35 l S S MATLAB 3 lo o l b U h co o 3 lo o b ol b C b o o LCG o cclc : 3 U 5 LSB o h c o 3 b < b q 53 b 8 q c cll CA o ~ 57 q5 c cll Ml Sbc wh Boow o ~ 3 S MATLAB wh o o o ~ 9 Mhwo cl ll h b bw Co o Slo o Coco S Sh EE I Gholo ll o b Go MATLAB o Go co o lh c lo c qll wh c o -53 lo o clol c co h o olo-o ll ow B Ml ho co ll o h wh o -53 Th wh MATLAB h oh h co co Th col o ch O wh : o l Th b h -c o h b O how h l qc o lo o b To El how h - o -53 S Slco: Eh h l o Clo o MATLAB h Cl ll o o cl h S cloc c b o 76 Co o Slo o Coco S Sh EE I Gholo ll o b Go MATLAB Dl o Go 7.78b l MTw 997 l o h: Po Ml cc o h ho oo col D o cl : I w loo h o wh 3-b ccc h o 63-l o o whol o q-b o 6-b ccc 6-l q-b 6-o o -b ccc 9968-o > 5 ol co MT cl h h b G. Ml >> ls S.DlS ls 9937 o c l S: Al: Z 77 Co o Slo o Coco S Sh EE I Gholo ll o b Go M Uo V o Ab PD boh col wh PSD C : CD o h V ow clo o lh Eol C : PD o h V ow clo o b o h CD G C 3: h PD o CD ow clo o I To Mho h ol. D : U P P U P U Th CD l ch l col U l Sc h o o-l PSD co. o boh El: β β β l U l U 78

7 Co o Slo o Coco S Sh EE I Gholo ll o b Go cl ll % b E b o o > ; 3; % ; % U _ q-**lo; % oo _ h_; % ho blo b_ % lo ho lbl b o Sl lbl I Vbl - blo.*; % o.*-; % lh l_ 3-; % b wh _h l ; % obbl o ho lo _h o % co l lbl Pobbl D lbl I Vbl - l l o ho b cl l C7_. 79 Co o Slo o Coco S Sh EE I Gholo ll o b Go M Uo V o Ab o Mho A w h l o c b ob c c b o Sl o o h ho P ob h h b P < c c P < P S: Ob U Sl o h - < 3 Ob o c l o h ho ccc U 8 Co o Slo o Coco S Sh EE I Gholo ll o b Go M Uo V o Ab co ccc Mho A o o M b S: Ob Sl o V ~ U V ~Ub wo cll o co I OW o o P ; ccc P ccc Pccc M M Aloh o c l. Wh b o l och Ecc M D b hl bo o b c b M b 8 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl I Mho co b o clo o o CD co Mho o c µ Q S o Uo B o Cl L Tho: U o bo B U E E B B hl o c Pobl: B c Tl obbl o o BE o Solo: b l c oc B.. B 6 B B Low h S c 8

8 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl U lh V Bo-Mll Mho o o- oll b I G Θ lh Uo Θ θ U U ~ U lu lu θ I Θ U cou Io DSP lo Slo θ lu U 83 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl U lh V Pol Mho Ml o o- oll b V V S ~ U V V I Co o BM : l S S V S lu - θ c wh o S ~ U P S < o h ccc o B colo o h Bo-Mll BM b l c Ecc 78.5% b o cll o o o o o lo o ooc co cou l S S V - lu U 8 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl MATLAB lo Ol MATLAB ol ho w MATLAB Dc Mho o o Z Aloh o Ml o 6 - cl o l o ll o h h o h cl < Ech cl c h l o Sb-cl W o <- - c b o cll ol oc: ϕ ϕ υ ϕ ϕ o56 obbl o o cl % ol A co b ho ACT6 Dw MATLAB 85 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl MATLAB lo O ch cll: A co o o cho ol U A o o l o h bcl o h cho co o U U ~ U < ; 3 Ohw oh o o. I h l w o ohw c { ϕ ϕ } U U ~ U < ϕ ϕ ; I h l co o > - o o oc El o l oc Ml o: V ~ U l V V M oh l oc V ~ U l V cc > ACT7 V h l oc 86

9 Co o Slo o Coco S Sh EE I Gholo ll o b Go Sl Poc w c o LTI o o oc Io c o co colo o o colo o b WSS * h h h E E E E S E Dl - Col S E E l h h h l h l h h * h l h l l h * 87 Co o Slo o Coco S Sh EE I Gholo ll o b Go G col G Sl S o o- o G : Z E Z E Z E Z E E Z G G wh b PSD o Aocolo Ucol l h wh PSD co lo BW: < S S S MATLAB l-wl ol -o co ch I l c DT o Sl S I G wll b G oo 88 Co o Slo o Coco S Sh EE I Gholo ll o b Go G b PSD PD Dl Scco Pobl I h G obl c o h o c o l c ch o cl Soh Aloh: A LTI ch h PSD o oh h wh c o MLL h PSD o LTI G G o Wh G LTI P-h l K PSD G Mo-l o-l. PSD: S PD: q K cho o h c cho o h ol c w h. cho o ch h So o bl 89 Co o Slo o Coco S Sh EE I Gholo ll o b Go G b PSD PD Dl Scco Pobl Th ch wo : ~ P. Z~ U ~ q. U G CD P o G Uo Z Po choc o co. o o h q P o : Z P ~ U Z ~ q P Q q E5:

10 o b Go o b Go G b PSD PD Dl Scco Pobl ow l how. c h PSD Bc o h o-l w oc h o Ao colo o : A c o wh colo coc : E Co o Slo o Coco S Sh E Polol : 9 EE I Gholo ll wh: o b Go o b Go G b PSD PD Dl Scco Pobl { } o ohool b o h lb c o h co : Wh h oc o A: < Co o Slo o Coco S Sh > < δ > < co lo: Solo o ODE o h o B: 9 EE I Gholo ll o b Go o b Go G b PSD PD Dl Scco Pobl Mhl Eo Tlo o co o c b w o h o o o C: Co o Slo o Coco S Sh 93 EE I Gholo ll o b Go o b Go G b PSD PD Dl Scco Pobl I h o l: Th w c w: Co o Slo o Coco S Sh W c cll h c b co o ch h Alo o h. o co o o o h o 9 EE I Gholo ll ϕ ϕ

11 Co o Slo o Coco S Sh EE I Gholo ll o b Go G b PSD PD Dl Scco Pobl A hoc: o b G w h: Tho: U o b : ± o c h o o o hh l o oo o. o l o Uo ' ' : G 95 Co o Slo o Coco S Sh EE I Gholo ll o b Go G b PSD PD Dl Scco Pobl C o Uo ' ' Mo l Soh : Σ : G Il o G o Σ M. M. Soh o Poc Wh Sc Scl D -O Pobbl D Bll S Tchcl Jol Vol h:b.bll-lb.cobstjvol6b Co o Slo o Coco S Sh EE I Gholo ll P Po ogo M Alco Coco S: Schoo DSSS I Slo h o o lco D Soc Mol Alo ll b cobo c b lh lo B o -b Sh Mol- Chcc olol G D D D... D D o M Tho: M Po - I chbl GD Poc l PSD wll b wh l L ll h GD D All obl cobo wll o o c o I o o b o o b o o - 97

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