Communication Theory II

Transcription

1 Cmmunicatin Thery II Lecture 2: Review n Furier analysis f signals and systems Ahmed Elnakib, PhD Assistant Prfessr, Mansura University, Egypt Febraury 12 th,

2 Quiz 1 In a blank paper write yur name and sectin number and list ne advantage f digital cmmunicatin systems Time: 2 min 2

3 Fast Overview 3

4 Required Curse Materials (updated) Text bks Sftware Other materials Simn Haykin, "Digital Cmmunicatin Systems, 1 st Editin," Wiley, 2013 MATLAB B. P. Lathi and Zhi Ding, Mdern Digital and Analg Cmmunicatin Systems, 4 th Editin Oxfrd Series in Electrical and Cmputer Engineering, S. Haykin, M. Mher, Cmmunicatin Systems, 5th Editin, Wiley, Michael Fitz, Fundamentals f Cmmunicatins Systems (Cmmunicatins Engineering), McGraw-Hill Prfessinal, 2007 Rbert G. Gallager, Principles f Digital Cmmunicatin, Cambridge University Press, MIT Curse Number 6.450: Principles f Digital Cmmunicatins I principles-f-digital-cmmunicatins-i-fall-2006/index.htm

5 Grading Assessment Methd Weights Time Mid Term Examinatin 20 Week 7 Oral Examinatin 10 Week 12 Semester wrk 20 Every week Final Term Examinatin 100 Week 14 Ttal 150 5

6 Oral Exam (10 marks) Objectives Ability t present yur self and yur ideas Ability t enhance creativity f individuals Ability t enhance searching capabilities f the students Ability t wrk in team 6

7 Oral Exam (Cnt d) Each sectin will be divided int grups, each grup is 3 t 5 persns Grup selectin (within the sectin) is ptinal till March 1st. After, the grup will be assigned by the alphabetic rder 7

8 Oral Exam (Cnt d) Each grup will design a suggested slutin fr a prblem in digital cmmunicatins and present the slutin in 4 slices as fllw: First slice cntains the title and the student names Secnd slice cntains the prblem t be slved and the traditinal slutin Third slice cntains a sketch f the prpsed slutin and/r needed materials Last slice cntains the reference list used in the prject An additinal slice can be added cntaining a simulatin if needed 8

9 Oral Exam (Cnt d) Each grup will take a 8-10 min presentatin exam, each student have t describe his rle in the prject Tw minutes fr questins Oral exam is ptinal fr students with excellent cntributins during the lectures r sectins 9

10 Hints fr a successful presentatin Wrk as a grup: distribute tasks Read well abut the tpic A gd presentatin is like a stry. The presenter gal is t present a cnnected lines fr the stry, while grapping the attentin f the audience Prepare yurself well, mst imprtantly, train well 10

11 Semester wrk (20 marks) Gal: Test the wrk f the students during the semester Online quiz/hmewrk [pen after the lecture (Thursday, 12 PM, nn) and clsed befre the sectin (Wednesday, 8 AM)] Small Quizzes inside the lectures and/r sectins 11

12 Curse Website The site cntains the lectures, quizzes, hmewrk, and pen frums fr feedback and questins Lg in using yur name and passwrd Passwrd fr quizzes: third 12

13 Curse Cntents* (updated) Intrductin t digital cmmunicatins Mathematics f digital cmmunicatins Furier analysis f signals and systems Prbability thery and Bayesian Interface Stchastic Prcesses Infrmatin thery Frm analg t digital cmmunicatins Wavefrm Cding Systems Digital Mdulatin/Demdulatin Signaling ver AWGN, band-limited, and fading channels Errr cntrl cding * 10% flexibility 13

14 Lecture Outlines Part 1: Cmmunicatins cncepts Multiple access techniques Cmputer netwrks Digital cmmunicatins Part II: Review n Furier analysis f signals and systems The Furier series The Furier transfrm 14

15 Multiple access techniques Frequency divisin multiple access (FDMA) Time divisin multiple access (TDMA) Cde divisin multiple access (CDMA) Space divisin multiple access (SDMA) 15

16 TDMA vs. FDMA (a) Time divisin multiple access (TDMA) and (b) frequency divisin multiple access (FDMA) * * Image curtesy f Simn Haykin, "Digital Cmmunicatin Systems, 1 st Editin," Wiley,

17 Cde divisin multiple access (CDMA) (a) (b) (a) Cde divisin multiple access (CDMA) and (b) an example f CDMA: frequency-hp multiple access * * Image curtesy f Simn Haykin, "Digital Cmmunicatin Systems, 1 st Editin," Wiley,

18 Space divisin multiple access (SDMA) SDMA separates users n shared frequencies by islating them with directinal antennas. Mst cell sites have three antenna arrays t separate their cverage int islated 120 sectrs (a). Adaptive arrays use beamfrming t pinpint desired users while ignring any thers n the same frequency (b)*. * Image curtesy f L. Frenzel, Fundamentals f Cmmunicatins Access Technlgies: FDMA, TDMA, CDMA, OFDMA AND SDMA Accmmdating multiple users in a single bandwidth is the essence f access methds,

19 Cmmunicatin Netwrks Intersectin f number f ndes (e.g., prcessrs) Nde: rute data thrugh the netwrk Statin: devices wishing t cmmunicate (e.g., user) * Image curtesy f Simn Haykin, "Digital Cmmunicatin Systems, 1 st Editin," Wiley,

20 Circuit switching vs. packet switching (a) (b) Circuit switching (link sharing is based n fixed allcatin) vs. packet switching (message is divided int segments r packets if necessary, sharing is per demand) * * Image curtesy f 20

21 Blck diagram f a digital cmmunicatin system* * Image curtesy f Simn Haykin, "Digital Cmmunicatin Systems, 1 st Editin," Wiley,

22 Blcks f a digital cmmunicatin system Surce encder: remve redundant infrmatin frm the message signal, utput: surce cdewrd Channel encder: prduce a new sequence f symbls adding channel cntrls and errr crrectins (channel cdewrd) Mdulatr: Represent each symbl f the channel cdewrd by crrespnding analg signal (wavefrm) amng a finite set f analg signals 22

23 Lecture Outlines Part 1: Cmmunicatins cncepts Multiple access techniques Cmputer netwrks Digital cmmunicatins Part II: Review n Furier analysis f signals and systems The Furier series The Furier transfrm 23

24 Furier transfrm Prvides the mathematical link between the time dmain f a signal (wavefrm) and its frequency dmain (spectrum) Time and frequency respnse f a linear time-invariant (LTI) system defined in terms f its impulse respnse and frequency respnse, respectively F F F -1 24

25 LTI system If and x 1 (n) h(n) y 1 (n) x 2 (n) h(n) y 2 (n) If x 1 (n) h(n) y 1 (n) Then x 1 (n-k) h(n) y 1 (n-k) Then a 1 y 1 (n)+a 2 y 2 (n)=h{a 1 x 1 (n)+a 2 x 2 (n)} Where a1, a2 are scalars (a) (b) A (a) linear and (b) a time invariant system 25

26 The Furier series Let dente a peridic signal, where the subscript T 0 dentes the duratin f peridicity. By using a Furier series expansin f this signal, we are able t reslve it int an infinite sum f sine and csine terms: Where is the fundamental frequency represent the amplitudes f the csine and sine terms, respectively are called basis functins 26

27 Basis functins ( ) Frm an rthgnal set ver the perid T 0 In that they satisfy three cnditins: 27

28 Mean value (a 0 ) and ther cefficients Integrate ver a cmplete perid bth sides f the equatin: yields: Other cefficients: 28

29 Existence f Furier series A peridic signal can be expanded in a Furier series if the signal satisfies the Dirichlet cnditins: Frm an engineering perspective, hwever, it suffices t say that the Dirichlet cnditins are satisfied by the peridic signals encuntered in cmmunicatin systems 29

30 Cmplex expnential Furier series Where Inner prduct f the signal with the basis functin [ ] 30

31 The Furier Transfrm Representatin f nn-peridic signals Derivatin is based n Furier series (text bk: page 16,17) 31

32 Existence f Furier Transfrm Physical realizability is a sufficient cnditin fr the existence f a Furier transfrm (e.g., all energy signals are Furier transfrmable ). Cnditin fr energy signal: 32

33 Furier Transfrm Prvides mathematical tls fr measuring the frequency cntent r spectrum f a signal G(f) is the Furier transfrm r the spectrum f the signal Simple evaluatin f magnitude spectrum G(f) and phase spectrum G(f) 33

34 Tables 34

35 Questins 35