1 / 79

TCOM 551 DIGITAL COMMUNICATIONS

TCOM 551 DIGITAL COMMUNICATIONS. SPRING 2005 IN 136 Wednesdays 4:30 – 7:10 p.m. Dr. Jeremy Allnutt jallnutt@gmu.edu. General Information - 1. Contact Information Room: Science & Technology II, Room 269 Telephone (703) 993-3969 Email: jallnutt@gmu.edu Office Manager: TBD

verena
Download Presentation

TCOM 551 DIGITAL COMMUNICATIONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. TCOM 551DIGITAL COMMUNICATIONS SPRING 2005 IN 136 Wednesdays 4:30 – 7:10 p.m. Dr. Jeremy Allnutt jallnutt@gmu.edu Lecture number 1

  2. General Information - 1 • Contact Information • Room: Science & Technology II, Room 269 • Telephone (703) 993-3969 • Email: jallnutt@gmu.edu • Office Manager: TBD • Office Hours • Mondays and Tuesdays 3:00 – 6:00 p.m.Please, by appointment only Lecture number 1

  3. Sorry: the web document is not yet up General Information - 2 • Course Outline • Go to http://telecom.gmu.eduand click oncourse schedule • Scroll down to TCOM 551 • Bad weather days: call (703) 993-1000 • You MUST Have The Following • Bateman Textbook, preferably also Kolimbiris • A Mathematical Calculator – please, simple ones only Lecture number 1

  4. General Information - 3 • Homework Assignments • Feel free to work together on these, BUT • All submitted work must be your own work • Web and other sources of information • You may use any and all resources, BUT • You must acknowledge all sources • You must enclose in quotation marks all parts copied directly – and you must give the full source information Lecture number 1

  5. No double jeopardy General Information - 4 • Exam and Homework Answers • For problems set, most marks will be given for the solution procedure used, not the answer • So: please give as much information as you can when answering questions: partial credit cannot be given if there is nothing to go on • If something appears to be missing from the question set, make – and give – assumptions used to find the solution Lecture number 1

  6. General Information - 5 • Term Paper • Any topic in field of Digital Communications • About 10 pages long + about 4 figures • Can work alone or in small groups (length of paper grows with number in group – with permission only) • Paper marks depend on delivery date(see slide 9) Possible Topics? Lecture number 1

  7. General Information - 6 • Examples of Term Paper Topics • TDMA vs. CDMA in various situations • LD-CELP: what is it and how does it help? • MPEG2: what is it and how does it help? • Digital Imaging and its impact on sports casting • DBS: why did digital succeed where analog failed • What is a smart antenna and how will it help? • UWB • Bluetooth vs. IEEE 802.11B Etc.!!! Lecture number 1

  8. General Information - 7 • Class Grades • Emphasis is on overall effort and results • Balance between homework, tests, paper + final exam: • Homework - 10% • Tests - 25 + 25% • Final exam - 30% • Term Paper - 10% maximum Lecture number 1

  9. Term Paper Grade Percentage • A mark will be allocated towards the grade as follows: • Prior to and on April 6th:  10% • Nov. 10th through April 13th:  8% • Nov. 17th through April 20th:  6% • Nov. 24th through May 27th:  3% • After April 27th: 0% Lecture number 1

  10. http://ece.gmu.edu/coursepages.htm TCOM 551 Course Plan Another alternative • Go to http://telecom.gmu.edu,click on course schedule, scroll down to TCOM 551 • In-Class Tests scheduled for - March 2nd - April 13th • In-Class Final exam scheduled for - May 11th Lecture number 1

  11. TCOM 551 Lecture 1 Outline • Sine Wave Review • Frequency, Phase, & Wavelength • Logarithms and dB (decibel) notation • Core Concepts of Digital Communications • Source info., Carrier Signal, Modulation • C/N, S/N, and BER • Performance & Availability Lecture number 1

  12. Sine Wave Review - 1 We all know that the Sine of an angle is the opposite side divided by the hypotenuse, i.e. B Sine (a) = A/B A Angle a But what happens if line B rotates about Point P? Point P Lecture number 1

  13. Sine Wave Review - 2 Line B now describes a circle about Point P B a What happens if we shine a light from the left and project the shadow of B onto a screen? Point P Lecture number 1

  14. Sine Wave Review - 3 End of “B” projected onto the screen B a Point P Light from the left Screen on the right Lecture number 1

  15. Sine Wave Review - 4 End of “B” projected onto the screen As line “B” rotates about the center point, P, the projected end of “B” oscillates up and down on the screen. What happens if we move the screen to the right and ‘remember’ where the projected end of “B” was? Screen on the right Lecture number 1

  16. Sine Wave Review - 5 Locus of “B” end-point We have a Sine Wave! One oscillation = One wavelength,  a.k.a. SHM ScreenPosition 1 ScreenPosition 2 Lecture number 1

  17. Sine Wave Review - 5 Remember:Sine 0 = 0; Sine 90 = 1; Sine 180 = 0; Since 270 = -1; Sine 360 = Sine 0 = 0 +1 0 90 180 270 360 Degrees -1 Lecture number 1

  18. Sine and Cosine Waves - 1 SineWave Sine Wave = Cosine Wave shifted by 90o 0o 90o 180o 270o 0 = 360o 90o 180o CosineWave Lecture number 1

  19. Sine and Cosine Waves - 2 Sine and Cosine waves can therefore be considered to be at right angles, i.e. orthogonal, to each other “Cosine Wave” Sine Wave Lecture number 1

  20. Sine and Cosine Waves - 3 • A Radio Signal consists of an in-phase component and an out-of-phase (orthogonal) component • Signal, S, is often written in the generic formS = A cos  + j B sin  Where j = ( -1 ) In-phase component Orthogonal component We will only consider Real signals Real Imaginary Lecture number 1

  21. Sine and Cosine Waves - 4 • Two concepts • The signal may be thought of as a time varying voltage, V(t) • The angle, , is made up of a time varying component,  t, and a supplementary value, , which may be fixed or varying • Thus we have a signalV(t) = A cos (t +) Lecture number 1

  22. Sine and Cosine Waves - 5 Vary these to Modulate the signal • Time varying signalV(t) = A cos (t +) Phase: PM; PSK Instantaneous value of the signal Frequency: FM; FSK Amplitude: AM; ASK Note:  = 2  f Lecture number 1

  23. Back to our Sine Wave – 1Defining the Wavelength The wavelength is usually defined at the “zero crossings”   Lecture number 1

  24. Back to our Sine Wave - 2 One revolution = 360oOne revolution also completes one cycle (or wavelength) of the wave.So the “phase” of the wave has moved from 0o to 360o (i.e. back to 0o ) in one cycle.The faster the phase changes, the shorter the time one cycle (one wavelength) takes Lecture number 1

  25. Back to our Sine Wave – 3Two useful equations The time taken to complete one cycle, or wavelength, is the period, T.Frequency is the reciprocal of the period, that isf = 1/T  Phase has changed by The rate-of-change of the phase, d/dt, is the frequency, f. Lecture number 1

  26. Before we look at d/dt, lets look at rate-of-change of phase Sine Wave – 4 • What do we mean “Rate-of-change of phase is frequency”? • One revolution = 360o = 2 radians • One revolution = 1 cycle • One revolution/s = 1 cycle/s = 1 Hz • Examples: • 720o/s = 2 revolutions/s = 2 Hz • 18,000o/s = 18,000/360 revs/s = 50 revs/s = 50 Hz  Lecture number 1

  27. d/dt Digression - 1 Person walks 16 km in 4 hours.Velocity = (distance)/(time)Therefore, Velocity = 16/4 = 4 km/hVelocity is really the rate-of-change of distance with time.What if the velocity is not constant? kilometers 1612840 0 1 2 3 4 5 6 7 8 9Time, hours Lecture number 1

  28. d/dt Digression - 2 kilometers You can compute the Average Velocity using distance/time,(i.e. 16/8 = 2 km/h), but how do you get the person’s speed at any particular point? 1612840 0 1 2 3 4 5 6 7 8 9Time, hours Answer: you differentiate, which means you find the slope of the line. Lecture number 1

  29. d/dt Digression - 3 kilometers To differentiate means to find the slope at any instant.The slope of a curve is given by the tangent at that point, i.e., A/BIn this case, A is in km and B is in hours. It could equally well be phase, , and time, t. 1612840 A B 0 1 2 3 4 5 6 7 8 9Time, hours Lecture number 1

  30. d/dt Digression - 4 • When we differentiate, we are taking the smallest increment possible of the parameter over the smallest interval of (in this case) time. • Small increments are written ‘d’(unit) • Thus: the slope, or rate-of-change, of the phase, , with time, t, is written as d/dt Lecture number 1

  31. Sine Wave Continued • Can think of a Sine Wave as a Carrier Signal,i.e. the signal onto which the information is loaded for sending to the end user • A Carrier Signal is used as the basis for sending electromagnetic signals between a transmitter and a receiver, independently of the frequency Lecture number 1

  32. Carrier signals - 1 • A Carrier Signal may be considered to travel at the speed of light, c, whether it is in free space or in a metal wire • Travels more slowly in most substances • The velocity, frequency, and wavelength of the carrier signal are uniquely connected byc = f  Wavelength Velocity of light Frequency Lecture number 1

  33. Carrier signals - 2 • Example • WAMU (National Public Radio) transmits at a carrier frequency of 88.5 MHz • What is the wavelength of the carrier signal? • Answer • c =(3×108) m/s = f ×= (88.5  106) × () • Which gives  = 3.3898 m = 3.4 m Remember: Make sure you are using the correct units Lecture number 1

  34. Digression - UNITS • Standard units to use are MKS • M = meters written as m • K = kilograms written as kgm • S = seconds written as s • Hence • the velocity of light is in m/s • The wavelength is in m • And the frequency is in Hz = hertz So: do not mix feet with meters and pounds with kilograms Lecture number 1

  35. Carrier signals - 3 • A Carrier Signal can • carry just one channel of information (this is often called Single Channel Per Carrier = SCPC) • Or carry many channels of information at the same time, usually through a Multiplexer Single Channel Note: The modulator has been omitted in these drawings Tx SCPC Multiplexer Multiplexed Carrier Multi-channel carrier Tx Lecture number 1

  36. Logarithms - 1 • The use of logarithms came about for two basic reasons: • A need to multiply and divide very large numbers • A need to describe specific processes (e.g. in Information Theory) that counted in different bases • Numbers are to the base 10; i.e. we count in multiples of tens Lecture number 1

  37. Logarithms - 2 • 1, 2, 3, 4, 5, 6, 7, 8, 9, 10To be easier to see, this should be written as the series00, 01, 02, 03, 04, 05, …. 09, 10 • 11, 12, 13, 14, 15 ….. • ….. • 91, ……, 97, 98, 99, 100 • … • 991, ….., 997, 998, 999, 1000 We actually count from 1 to 10 but the numbering goes from 0 to 9, then we change the first digit and go from 0 to 9 again, and so on Lecture number 1

  38. Logarithms - 3 • Counting to base 10 is the Decimal System • We could equally well count in a Duodecimal System, which is a base 12, a Hexadecimal System, which is a base 16, a Binary System, which is a base 2, etc. • Sticking with the Decimal System Lecture number 1

  39. Logarithms – 4A • A Decimal System can be written as a power of 10, for example • 100 = 1 • 101 = 10 • 102 = 100 • 103 = 1,000 • 104 = 10,000 Lecture number 1

  40. Logarithms – 4B • A Decimal System can be written as a power of 10, for example • 100 = 1 • 101 = 10 • 102 = 100 • 103 = 1,000 • 104 = 10,000 Do you detect any logic here? Lecture number 1

  41. Logarithms – 4C • A Decimal System can be written as a power of 10, for example • 100 = 1 • 101 = 10 • 102 = 100 • 103 = 1,000 • 104 = 10,000 Do you detect any logic here? The number of zeroes is the same as the value of the exponent Lecture number 1

  42. Logarithms - 5 • Let’s look at these again • 100 = 1 • 101 = 10 • 102 = 100 • 103 = 1,000 • 104 = 10,000 The exponent is called the logarithm of the number That is:The logarithm of 1 = 0The logarithm of 10 = 1The logarithm of 100 = 2, etc. Lecture number 1

  43. Logarithms - 6 • Question: • The logarithm of 1 to the base 10 (written as log101) = 0 and log1010 = 1. What if I want the logarithm of a number between 1 and 10? • Answer: • You know the answer must lie between 0 and 1 • The answer = x, where x is the exponent of 10 • Ummmmmh???? We’ll do an example Lecture number 1

  44. Logarithms - 7 • Question • What is the logarithm of 3? • Answer: • We want log103 • Let log103 = x • Transposing, we have 10x = 3 • And 100.4771213 = 3, giving x = 0.4771 • Thus log103 = 0.4771 Lecture number 1

  45. Logarithms - 8 • More Examples • What is log10 4? • What is log10 7? • What is log10 7.654? • What is log10 24? • What is log10 4123.68? • What is log10 0.69? Lecture number 1

  46. Logarithms - 9 • More Examples (Answers) • What is log10 4? = 0.6021 • What is log10 7? = 0.8451 • What is log10 7.654? = 0.8839 • What is log10 24? = 1.3802 • What is log10 4123.68? = 3.6153 • What is log10 0.69? = -0.1612 0.69 is < 1 so the answer must be below 0 Lecture number 1

  47. Logarithms - 10 • Question • What if I want to have a logarithm of the value “x” with a different base? • Answer • Let’s assume you want to have loga of x, i.e. the base is “a” and not 10 • Then logax =(log10 x) / (log10 a) Example Lecture number 1

  48. Logarithms - 11 • Question • What is log2 10?(i.e. base “a” = 2 and the number x =10) • Answer • Since loga x =(log10 x) / (log10 a) • Log210 = (log1010) / (log102) = 1/0.301 = 3.3219 Lecture number 1

  49. Logarithms - 12 • Let’s look at this another way: • Log2 10 = 3.3219 • Remember, if loga (number) = x, we can transpose this to ax = (number) • Thus, another way of looking at • Log2 10 = 3.3219 is to write • 23.3219 = 10 But what if the exponent is always a whole number? Lecture number 1

  50. Logarithms - 13 • 20 = 1 log2 1 = 0 • 21 = 2 log2 2 = 1 • 22 = 4 log2 4 = 2 • 23 = 8 log2 8 = 3 • 24 = 16 log2 16 = 4 • 25 = 32 log2 32 = 5 • 26 = 64 log2 64 = 6 This is the Binary System Log2 is fundamental to Information Theory Lecture number 1

More Related