ECE 3TR4 Communication Systems (Winter 2004)

Transcription

1 ECE 3R4 Communicaion Sysms Winr 4 Dr.. Kirubarajan Kiruba ECE Dparmn CRL-5 iruba@mcmasr.ca

2 Cours Ovrviw Communicaion Sysms Ovrviw Fourir Sris/ransorm Rviw Signals and Sysms Rviw Inroducion o Nois Moivaion or Modulaion Ampliud Modulaion Angl Modulaion Puls Modulaion Muliplxing ransmirs and Rcivrs J Bondy

3 Communicaion Sysms Inormaion Sourc ransmir Channl Rcivr Inormaion Dsinaion Blacbrry Kypad GSM-syl RF Wirlss RF FM Dcor AM.5 Pac Spars Brain Vocal rac Acousic Ears Brain IP Pac SONE Rour Fibr Phoo Diod Rour POS Analog Communicaions 3R4: Inormaion is ncodd in a coninuous ampliud, coninuous im signal. Digial Communicaions 4K4: Inormaion is ncodd ino a discr im squnc wih a quanizd alphab. J Bondy 3

4 Communicaion Channls Channl: h mdium lining h ransmir and rcivr. I is ALWAYS analog in naur. ha is vry communicaion sysm is mor or lss ANALOG. Channl yps Wirlin Channls: us a conduciv mdium o dirc ransmid nrgy o h rcivr: Coppr wir or lphons, xdsl Fibr opic cabl Aluminum inrconncs or ICs Wirlss Channls: Uss an opn propagaion mdium RF or cll phons Undrwar acousic ducs or whals J Bondy 4

5 Channl Impairmns As a ransmid signal propagas i loss idliy in a numbr o ways. his loss o idliy mas h rcivd signal loo vry dirn rom h ransmid signal. Addiiv Nois: hrmal nois, muli-ransmir inrrnc Nois ransmir + Rcivr Muliplicaiv Nois: Rayligh Fading Nois ransmir x Rcivr Convoluion Nois: im-dlay mulipah, rvrbraion ransmir Nois Rcivr J Bondy 5

6 3R4 Objciv Inormaion Sourc ransmir Channl Rcivr Inormaion Dsinaion. How o dsign. aing ino accoun 3. ha will provid a sysm ha is: Rliabl: inormaion rcivd is wha was sn Eicin: No wasul o im, powr or spcrum Simpl: conomical or H/W and S/W and usually Robus J Bondy 6

7 rados in Objcivs mporal Us Spcral Us Powr Us Eicin Simpl H/W Simpl S/W Simpl Rliabl Accuracy & Robusnss J Bondy 7

8 Digial Communicaions Digial Inormaion Sourc N Sourc Encodr Channl Encodr DAC Modulaor h placmn o h DAC and ADC is up o h sysm rquirmns. hy can b anywhr bwn h Inormaion Sourcs and Dsinaion and h Modulaor and Dmodulaor, rspcivly. Channl Digial Inormaion Dsinaion Sourc Dcodr Channl Dcodr ADC DModulaor J Bondy 8

9 Fourir Sris/ransorm Rviw 9

10 Fourir Rviw Fourir Sris and ransorms ry o orm a signal ou o sinusoids. hs sinusoids hav a spciic rquncy and go on orvr. ha is your nic im sris which is rprsnd by poins in im will now b rprsnd by poins in rquncy. his is why w us h rms Fourir domain and rquncy domain inrchangably. Rmindr: a jb a cos b + ja sin b J Bondy

11 Wha ransorm, Whn? Sar Domain Discr or Coninuous Priodic ransorm im Discr Ys DFS im Discr No DF im Coninuous Ys FS im Coninuous No F Frquncy Discr Ys I-DFS Frquncy Discr No I-FS Frquncy Coninuous Ys I-DF Frquncy Coninuous No I-F J Bondy

12 Discr im Fourir Sris DFS: I-DFS: jω X[ ] n < N > x[ n] N jω x[ n] < N > X[ ] N n n X[] and x[n] hav priod N Ω π/n J Bondy

13 3 J Bondy Discr im Fourir ransorm Ω Ω n n j j n x X ] [ ] [ Ω Ω Ω π π π d X n x n j j ] [ DF: I-DFS: X[] has priod π

14 Fourir Sris FS: j X[ ] x < > d I-FS: x X[ ] j o X has priod Ω π/ J Bondy 4

15 Fourir ransorm F: I-F: X x j x d j j X j d π h Fourir ransorm is h gnral ransorm, i can handl priodic and non-priodic signals. For a priodic signal i can b hough o as a ransormaion o h Fourir Sris X j π X[ ] δ n J Bondy 5

16 6 J Bondy Fourir Sris > < j d x X ] [ B o A o d x j d x X > < > < sin cos ] [ X B A X A B X θ θ + an ] [

17 x Fourir Sris Ral Signals X[ ] x cos o d j x sin o d < > < > A B I x is ral valud: A A - B -B - X[ ] x X[] + x X[] + j o X[] + jo jo jo jo X[ ] + X[ ] X[] + A + jb + A + jb jo jo jo jo jo jo A + jb + A jb X[] + A + + jb + jo A cos + B sin X[] + R X[ ] o o x + X [] R X [ j j o ] θ X[] + X[ ] cos + θ J Bondy 7

18 Fourir Sris Ral +Evn/Odd x X [] + x X[] + x X[] + R X [ j j ] θ o R { A jb cos + j sin } A cos + B sin Evn: -, hror B ; Cosin Sris Odd: --, hror A ; Sin Sris o o o o J Bondy 8

19 Cosin Fourir Sris j j cos + Evn Funcion FS F πfs X[ ] X[ ] X j πδ + + πδ Whn is F h coninuous counrpar o πfs? How do h Dla s mov as rquncy changs? J Bondy 9

20 Sin Fourir ransorm j j sin Odd Funcion FS F πfs j j X[ ] X[ ] j X j jπδ + jπδ h Fourir ransorm o an Odd Signal is Odd. Noic h Fourir Domain graph is in jf. I is imaginary. J Bondy

21 DC Fourir ransorm DC Funcion FS F FS j ; F X[ ] X j πδ h F o a signal wih a DC componn is sparabl. h DC componn o a im signal is saisically h MEAN. X j π X[ ] δ J Bondy

22 Dla Fourir ransorm Dla Funcion F FS δ - No Fourir Sris, No Priodic X j jπ jπ δ d h F is only congrun wih h FS or PERIODIC signals. A dla has an ininily sp ris im, hror i has a gra dal o high rquncis J Bondy

23 Puls rain Fourir ransorm X n δ n Funcion wih Priod FS X[ ] j n δ n j π j πn π d or n all d Wha happns in h Frquncy Domain whn h im bwn pulss is shornd? Whn? Whn? δ π J Bondy 3

24 im Window Fourir ransorm, < τ, τ No Priodic No FS sinτ F X j τ Sinc τ sin x Sinc x Sa x rc τ x J Bondy 4

25 Idal Filr Fourir ransorm x Sinc W No Priodic No FS F π, < W X j W π rc, W W W Why is his calld h idal ilr? Noic similariis bwn his and rcangular im window, and how W hr is a counrpar o τ hr in conrolling widh. J Bondy 5

26 riangl Fourir ransorm x, τ, No Priodic No FS < τ τ [ ] Λ F X j τ Sinc τ Sinc squard can nvr b ngaiv. Why ar w inroducing hs signals? hy ar h oundaion o mos analog communicaion signals. τ J Bondy 6

27 Mor Complx Exampl An puls rain wih priod on scond is convolvd wih a im windowing uncion wih iming τ o.5 sconds, o produc a 5% duy cycl squar wav. J Bondy 7

28 Mor Complx Exampl h spcrum o h puls rain is: π X j π δ h spcrum o h squar-wav is: X j τ Sinc τ Convoluion urns ino Muliplicaion in h Frq Domain τ δ π X j X j πτ Sinc his urns ino a lin spcra, and how i changs wih changing h paramrs is vry inormaiv J Bondy 8

29 Consan τ τ Ampliud DECREASES as / Lin spcra rsoluion INCREASES as h nvlop is INDEPENDEN o J Bondy 9

30 Consan τ.5 τ.5 τ Ampliud INCREASES in proporion o au Lin spcra rsoluion is INDEPENDEN o au h spcrum SPREADS as h window shorns!!! IME RESOLUION AND FREQUENCY RESOLUION ARE INVERSELY RELAED!!!!!!!! J Bondy 3

31 h Sampling horm On o h undamnal concps in daling wih h rprsnaion o analog signals in h digial domain is h Nyquis Ra, or Minimum im-bandwidh produc. his law sas h minimum sampl rquncy ncssary o xacly rprsn an analog signal as a digial signal. Sinc on o h main consrains in judging h icincy o a communicaion sysm is spcral icincy, h Nyquis ra orms a larg par o h bac-bon o sysm dsign. A ral-valud band-limid signal having no spcral componns abov a rquncy o B Hz is drmind uniquly by is valus a uniorm inrvals spacd no grar han /B sconds apar J Bondy 3

32 3 J Bondy Sampling horm Considr a signal sampld wih an impuls rain p n s n s n jn s n jn s n F F n F F ransorm Fourir p p,, δ π

33 Sampling horm Visual Band limid signal + spcrum Priodic gaing uncion + spcrum Siz o sampling window conrols nvlop o spcrum, sampl rquncy conrols spacing o original spcrum rplicas J Bondy 33

34 Nyquis Ra Sinc h priodic gaing uncion conrols h cnr o h rplicas and h rplicas ar W W πb wid, hn o ma sur hr is no ovrlap: π W B I h signal is sampld a a lowr ra hr will b ovrlap, and in h inal spcrum you won now i h ovrlappd par is rom h spcrum ha is suppos o b hr or rom h ALIASED par o h spcrum J Bondy 34

35 Signals and Sysms Rviw 35

36 Enrgy and Powr Signal Enrgy E Signal Powr P * d, UNIS [ V s] lim * d, UNIS [ V An nrgy signal canno b a powr signal, nor vic-vrsa o b an nrgy signal: Ampliud As im in ] J Bondy 36

37 37 J Bondy Enrgy and Powr Exampl Find E x x x A A E d A d A E A x φ φ φ φ sin 4 cos cos cos sin sin 4 cos cos / / / / lim lim lim A A A P d A d A P x x φ φ φ φ

38 38 J Bondy Parsval s horm Enrgy calculad in h im domain is qual o nrgy calculad in h Frquncy domain. π π π π π d F F d d F d d F d d d F d d F d F F d j j j j * * * * * * * * * *

39 39 J Bondy Powr Spcral Dnsiy π π d S P d F P / / lim F S d dg du u F du u S G du u F du u S G d F d S lim lim lim lim π π π π π π

40 PSD S is h powr spcral dnsiy uncion, i has unis o powr pr Hz. G is h cumulaiv spcral powr uncion, i h amoun o nrgy in h signal in hos componns lss hn. J Bondy 4

41 4 J Bondy Auocorrlaion { } { } { } { } { } / / * / / / / * / / / / * / / / / * * lim lim lim lim lim lim τ τ τ δ π π π τ τ τ j j j j j R d S IF d d S IF d d d S IF d d d S IF d F F S IF F S + + +

42 Auocorrlaion R τ should loo amiliar in a way. I is quivaln o convolving h uncion wih -. R * τ lim τ τ / / * + τ d + τ d h auocorrlaion uncion is on usd or signal dcion in a bacground o random nois. Whn w g ino random nois i will bcom vry vidn why his is so. J Bondy 4

43 Linar im Invarian Sysms Fundamnal way o dscribing many componns in a communicaion sysm. Modls ilrs, ampliirs and qualizrs vry wll. Modl an LI sysm wih h impuls rspons, h, o h sysm, h rspons o an impuls inpu o h sysm. h Fourir ransorm o h impuls rspons is h rquncy ransr uncion. y h x x h y h τ x τ dτ J Bondy 43

44 im Opraors g -a g +b g/ Wha happns o in h Fourir domain o ach o hs? J Bondy 44

45 Invribiliy LI sysms ar invribl I you can drmin h inpu givn h oupu hn a sysm is calld Invribl Givn inpu x and i s oupu is y: y x Is invrd by z: z ½ y x No invribl: y loor{x}!!! A non-invribl sysm usually maps mulipl poins rom h inpu spac o h sam poin in h oupu spac. J Bondy 45

46 46 J Bondy LI Sysms x h y x y h X H Y X Y H In h rquncy domain h convoluion ingral bcoms a muliplicaion, and vic-vrsa. By assssing h rquncy domain magniud and phas w can s how H can c spciic rquncis dirnly: θ θ θ θ θ θ x h y j j j X H Y X H Y x h y +!!! his is h bginning o h ilring inrpraion

47 LI Sysms h Law o Suprposiion: Givn inpus a and b o sysm x, a linar sysm: xa+xb xa+b Givn inpu a and som scalar consan o sysm x, xc a c xa h Law o im Invarianc: Givn som inpu uncion g and is inpu o a sysm X producs an oupu X{g} I g is shid in im by hn h oupu has h sam shi X{g- } - h Law o Commuaion: Givn som uncion g and g * * g J Bondy 47

48 Idal Filr Inroducion Frquncy Rspons Impuls Rspons Low Pass Filr LPF High Pass Filr HPF BandPass Filr BPF BandSop Filr BSF J Bondy 48

49 Ral Filrs In raliy on canno ma h Bric Wall yp idal ilrs. his is du o h undamnal rado bwn im and rquncy rsoluion. I you hav a jump in h rquncy rspons ha is ininisimally rsolvd, you d nd inini im o rprsn ha. On dals wih ilr spciicaions such as bandwidh, rollo, implmnaion complxiy, passband rippl and so on or mos o his cours, and or many uur courss. I is o gra pracical imporanc o undrsand h rados implici in h im-rquncy bandwidh rado. J Bondy 49

50 Filrs con d Mos ilrs bandwidhs ar dind by h 3 db poin, or whr h rquncy ransr rspons is / lss hn h maximum poin. J Bondy 5

51 Filr runcaion - im On can nvr implmn an idal ilr bcaus h inini rquncy rsoluion rquirs inini im. Wha happns whn you jus g rid o som o h im window? W Ringing Gibbs c Longr im Window, spr rquncy roll-o J Bondy 5