1. COE 342: Data & Computer Communications (T042) Dr. Marwan Abu-Amara Chapter 3: Data Transmission

2. COE 342 (T042) – Dr. Marwan Abu-Amara 2 Agenda Concepts & Terminology Decibels and Signal Strength Fourier Analysis Analog & Digital Data Transmission Transmission Impairments Channel Capacity

3. COE 342 (T042) – Dr. Marwan Abu-Amara 3 Terminology (1) Transmitter Receiver Medium  Guided medium e.g. twisted pair, optical fiber  Unguided medium e.g. air, water, vacuum

4. COE 342 (T042) – Dr. Marwan Abu-Amara 4 Terminology (2) Direct link  No intermediate devices Point-to-point  Direct link  Only 2 devices share link Multi-point  More than two devices share the link

5. COE 342 (T042) – Dr. Marwan Abu-Amara 5 Terminology (3) Simplex  One direction e.g. Television Half duplex  Either direction, but only one way at a time e.g. police radio Full duplex  Both directions at the same time e.g. telephone

6. COE 342 (T042) – Dr. Marwan Abu-Amara 6 Frequency, Spectrum and Bandwidth Time domain concepts  Analog signal Varies in a smooth way over time  Digital signal Maintains a constant level then changes to another constant level  Periodic signal Pattern repeated over time  Aperiodic signal Pattern not repeated over time

7. COE 342 (T042) – Dr. Marwan Abu-Amara 7 Analogue & Digital Signals

8. COE 342 (T042) – Dr. Marwan Abu-Amara 8 Periodic Signals

9. COE 342 (T042) – Dr. Marwan Abu-Amara 9 Sine Wave Peak Amplitude (A)  maximum strength of signal  volts Frequency (f)  Rate of change of signal  Hertz (Hz) or cycles per second  Period = time for one repetition (T)  T = 1/f Phase (  )  Relative position in time

10. COE 342 (T042) – Dr. Marwan Abu-Amara 10 Varying Sine Waves s(t) = A sin(2  ft +  )

11. COE 342 (T042) – Dr. Marwan Abu-Amara 11 Wavelength Distance occupied by one cycle Distance between two points of corresponding phase in two consecutive cycles Assuming signal velocity v  = vT  f = v  c = 3*10 8 m/sec (speed of light in free space)

12. COE 342 (T042) – Dr. Marwan Abu-Amara 12 Frequency Domain Concepts Signal usually made up of many frequencies Components are sine waves Can be shown (Fourier analysis) that any signal is made up of component sine waves Can plot frequency domain functions

13. COE 342 (T042) – Dr. Marwan Abu-Amara 13 Addition of Frequency Components (T=1/f)

14. COE 342 (T042) – Dr. Marwan Abu-Amara 14 Frequency Domain Representations

15. COE 342 (T042) – Dr. Marwan Abu-Amara 15 Spectrum & Bandwidth Spectrum  range of frequencies contained in signal Absolute bandwidth  width of spectrum Effective bandwidth  Often just bandwidth  Narrow band of frequencies containing most of the energy DC Component  Component of zero frequency

16. COE 342 (T042) – Dr. Marwan Abu-Amara 16 Decibels and Signal Strength Decibel is a measure of ratio between two signal levels  N dB = number of decibels  P 1 = input power level  P 2 = output power level Example:  A signal with power level of 10mW inserted onto a transmission line  Measured power some distance away is 5mW  Loss expressed as N dB =10log(5/10)=10(-0.3)=-3 dB

17. COE 342 (T042) – Dr. Marwan Abu-Amara 17 Decibels and Signal Strength Decibel is a measure of relative, not absolute, difference  A loss from 1000 mW to 500 mW is a loss of 3dB  A loss of 3 dB halves the power  A gain of 3 dB doubles the power Example:  Input to transmission system at power level of 4 mW  First element is transmission line with a 12 dB loss  Second element is amplifier with 35 dB gain  Third element is transmission line with 10 dB loss  Output power P2 (-12+35-10)=13 dB = 10 log (P 2 / 4mW) P 2 = 4 x 10 1.3 mW = 79.8 mW

18. COE 342 (T042) – Dr. Marwan Abu-Amara 18 Relationship Between Decibel Values and Powers of 10 Power Ratio dB dB 10 1 1010 -1 -10 10 2 2010 -2 -20 10 3 3010 -3 -30 10 4 4010 -4 -40 10 5 5010 -5 -50 10 6 6010 -6 -60

19. COE 342 (T042) – Dr. Marwan Abu-Amara 19 Decibel-Watt (dBW) Absolute level of power in decibels Value of 1 W is a reference defined to be 0 dBW Example:  Power of 1000 W is 30 dBW  Power of 1 mW is –30 dBW

20. COE 342 (T042) – Dr. Marwan Abu-Amara 20 Decibel & Difference in Voltage Decibel is used to measure difference in voltage. Power P=V 2 /R Decibel-millivolt (dBmV) is an absolute unit with 0 dBmV equivalent to 1mV.  Used in cable TV and broadband LAN

21. COE 342 (T042) – Dr. Marwan Abu-Amara 21 Fourier Analysis Signals Periodic (f o ) Aperiodic Discrete Continuous DFSFS DTFT FT DFT Infinite time Finite time FT: Fourier Transform DFT: Discrete Fourier Transform DTFT: Discrete Time Fourier Transform FS: Fourier Series DFS: Discrete Fourier Series

22. COE 342 (T042) – Dr. Marwan Abu-Amara 22 Fourier Series Any periodic signal can be represented as sum of sinusoids, known as Fourier Series If A 0 is not 0, x(t) has a DC component DC Component fundamental frequency

23. COE 342 (T042) – Dr. Marwan Abu-Amara 23 Fourier Series Amplitude-phase representation

24. COE 342 (T042) – Dr. Marwan Abu-Amara 24

25. COE 342 (T042) – Dr. Marwan Abu-Amara 25 Fourier Series Representation of Periodic Signals - Example 1 1/2-1/213/2-3/22 T x(t) Note:(1) x(– t)=x(t)  x(t) is an even function (2) f 0 = 1 / T = ½

26. COE 342 (T042) – Dr. Marwan Abu-Amara 26 Fourier Series Representation of Periodic Signals - Example Replacing t by –t in the first integral sin(-2  nf t)= - sin(2  nf t)

27. COE 342 (T042) – Dr. Marwan Abu-Amara 27 Fourier Series Representation of Periodic Signals - Example Since x(– t)=x(t) as x(t) is an even function, then B n = 0 for n=1, 2, 3, …

28. COE 342 (T042) – Dr. Marwan Abu-Amara 28 Another Example 1 1 2 T -2 x1(t) Note that x1(-t)= -x1(t)  x(t) is an odd function Also, x1(t)=x(t-1/2)

29. COE 342 (T042) – Dr. Marwan Abu-Amara 29 Another Example

30. COE 342 (T042) – Dr. Marwan Abu-Amara 30 Fourier Transform For a periodic signal, spectrum consists of discrete frequency components at fundamental frequency & its harmonics. For an aperiodic signal, spectrum consists of a continuum of frequencies.  Spectrum can be defined by Fourier transform  For a signal x(t) with spectrum X(f), the following relations hold

31. COE 342 (T042) – Dr. Marwan Abu-Amara 31

32. COE 342 (T042) – Dr. Marwan Abu-Amara 32 Fourier Transform Example x(t) A

33. COE 342 (T042) – Dr. Marwan Abu-Amara 33 Fourier Transform Example

34. COE 342 (T042) – Dr. Marwan Abu-Amara 34 Signal Power A function x(t) specifies a signal in terms of either voltage or current Instantaneous power of a signal is related to average power of a time-limited signal, and is defined as For a periodic signal, the average power in one period is

35. COE 342 (T042) – Dr. Marwan Abu-Amara 35 Power Spectral Density & Bandwidth Absolute bandwidth of any time-limited signal is infinite. Most power in a signal is concentrated in finite band. Effective bandwidth is the spectrum portion containing most of the power. Power spectral density (PSD) describes power content of a signal as a function of frequency

36. COE 342 (T042) – Dr. Marwan Abu-Amara 36 Power Spectral Density & Bandwidth For a periodic signal, power spectral density is where  (f) is

37. COE 342 (T042) – Dr. Marwan Abu-Amara 37 Power Spectral Density & Bandwidth For a continuous valued function S(f), power contained in a band of frequencies f 1 < f < f 2 For a periodic waveform, the power through the first j harmonics is

38. COE 342 (T042) – Dr. Marwan Abu-Amara 38 Power Spectral Density & Bandwidth - Example Consider the following signal The signal power is

39. COE 342 (T042) – Dr. Marwan Abu-Amara 39 Fourier Analysis Example Consider the half-wave rectified cosine signal from Figure B.1 on page 793: 1. Write a mathematical expression for s(t) 2. Compute the Fourier series for s(t) 3. Find the total power of s(t) 4. Find a value of n such that Fourier series for s(t) contains 95% of the total power in the original signal 5. Write an expression for the power spectral density function for s(t)

40. COE 342 (T042) – Dr. Marwan Abu-Amara 40 Example (Cont.) 1. Mathematical expression for s(t):

41. COE 342 (T042) – Dr. Marwan Abu-Amara 41 Example (Cont.) 2. Fourier Analysis:

42. COE 342 (T042) – Dr. Marwan Abu-Amara 42 Example (Cont.) 2. Fourier Analysis (cont.):

43. COE 342 (T042) – Dr. Marwan Abu-Amara 43 Example (Cont.) 2. Fourier Analysis (cont.):

44. COE 342 (T042) – Dr. Marwan Abu-Amara 44 Example (Cont.) 2. Fourier Analysis (cont.):

45. COE 342 (T042) – Dr. Marwan Abu-Amara 45 Example (Cont.) 2. Fourier Analysis (cont.):

46. COE 342 (T042) – Dr. Marwan Abu-Amara 46 Example (Cont.) 2. Fourier Analysis (cont.):

47. COE 342 (T042) – Dr. Marwan Abu-Amara 47 Example (Cont.) 2. Fourier Analysis (cont.):

48. COE 342 (T042) – Dr. Marwan Abu-Amara 48 Example (Cont.) 3. Total Power:

49. COE 342 (T042) – Dr. Marwan Abu-Amara 49 Example (Cont.) 4. Finding n such that we get 95% of total power:

50. COE 342 (T042) – Dr. Marwan Abu-Amara 50 Example (Cont.) 4. Finding n such that we get 95% of total power:

51. COE 342 (T042) – Dr. Marwan Abu-Amara 51 Example (Cont.) 4. Finding n such that we get 95% of total power:

52. COE 342 (T042) – Dr. Marwan Abu-Amara 52 Example (Cont.) 5. Power Spectral Density function (PSD): Or more accurately:

53. COE 342 (T042) – Dr. Marwan Abu-Amara 53 Example (Cont.) 5. Power Spectral Density function (PSD):

54. COE 342 (T042) – Dr. Marwan Abu-Amara 54 Signal with DC Component

55. COE 342 (T042) – Dr. Marwan Abu-Amara 55 Data Rate and Bandwidth Any transmission system has a limited band of frequencies This limits the data rate that can be carried Example on pages 65 & 66

56. COE 342 (T042) – Dr. Marwan Abu-Amara 56 Analog and Digital Data Transmission Data  Entities that convey meaning Signals  Electric or electromagnetic representations of data Transmission  Communication of data by propagation and processing of signals

57. COE 342 (T042) – Dr. Marwan Abu-Amara 57 Analog and Digital Data Analog  Continuous values within some interval  e.g. sound, video Digital  Discrete values  e.g. text, integers

58. COE 342 (T042) – Dr. Marwan Abu-Amara 58 Acoustic Spectrum (Analog)

59. COE 342 (T042) – Dr. Marwan Abu-Amara 59 Analog and Digital Signals Means by which data are propagated Analog  Continuously variable  Various media wire, fiber optic, space  Speech bandwidth 100Hz to 7kHz  Telephone bandwidth 300Hz to 3400Hz  Video bandwidth 4MHz Digital  Use two DC components

60. COE 342 (T042) – Dr. Marwan Abu-Amara 60 Advantages & Disadvantages of Digital Cheaper Less susceptible to noise Greater attenuation  Pulses become rounded and smaller  Leads to loss of information

61. COE 342 (T042) – Dr. Marwan Abu-Amara 61 Attenuation of Digital Signals

62. COE 342 (T042) – Dr. Marwan Abu-Amara 62 Components of Speech Frequency range (of hearing) 20Hz-20kHz  Speech 100Hz-7kHz Easily converted into electromagnetic signal for transmission Sound frequencies with varying volume converted into electromagnetic frequencies with varying voltage Limit frequency range for voice channel  300-3400Hz

63. COE 342 (T042) – Dr. Marwan Abu-Amara 63 Conversion of Voice Input into Analog Signal

64. COE 342 (T042) – Dr. Marwan Abu-Amara 64 Video Components USA - 483 lines scanned per frame at 30 frames per second  525 lines but 42 lost during vertical retrace So 525 lines x 30 scans = 15750 lines per second  63.5  s per line  11  s for retrace, so 52.5  s per video line Max frequency if line alternates black and white Horizontal resolution is about 450 lines giving 225 cycles of wave in 52.5  s Max frequency of 4.2MHz

65. COE 342 (T042) – Dr. Marwan Abu-Amara 65 Binary Digital Data From computer terminals etc. Two dc components Bandwidth depends on data rate

66. COE 342 (T042) – Dr. Marwan Abu-Amara 66 Conversion of PC Input to Digital Signal

67. COE 342 (T042) – Dr. Marwan Abu-Amara 67 Data and Signals Usually use digital signals for digital data and analog signals for analog data Can use analog signal to carry digital data  Modem Can use digital signal to carry analog data  Compact Disc audio

68. COE 342 (T042) – Dr. Marwan Abu-Amara 68 Analog Signals Carrying Analog and Digital Data

69. COE 342 (T042) – Dr. Marwan Abu-Amara 69 Digital Signals Carrying Analog and Digital Data

70. COE 342 (T042) – Dr. Marwan Abu-Amara 70 Analog Transmission Analog signal transmitted without regard to content May be analog or digital data Attenuated over distance Use amplifiers to boost signal Also amplifies noise

71. COE 342 (T042) – Dr. Marwan Abu-Amara 71 Digital Transmission Concerned with content Integrity endangered by noise, attenuation etc. Repeaters used Repeater receives signal Extracts bit pattern Retransmits Attenuation is overcome Noise is not amplified

72. COE 342 (T042) – Dr. Marwan Abu-Amara 72 Advantages of Digital Transmission Digital technology  Low cost LSI/VLSI technology Data integrity  Longer distances over lower quality lines Capacity utilization  High bandwidth links economical  High degree of multiplexing easier with digital techniques Security & Privacy  Encryption Integration  Can treat analog and digital data similarly

73. COE 342 (T042) – Dr. Marwan Abu-Amara 73 Transmission Impairments Signal received may differ from signal transmitted Analog - degradation of signal quality Digital - bit errors Caused by  Attenuation and attenuation distortion  Delay distortion  Noise

74. COE 342 (T042) – Dr. Marwan Abu-Amara 74 Attenuation Signal strength falls off with distance Depends on medium Received signal strength:  must be enough to be detected  must be sufficiently higher than noise to be received without error Attenuation is an increasing function of frequency

75. COE 342 (T042) – Dr. Marwan Abu-Amara 75 Delay Distortion Only in guided media Propagation velocity varies with frequency

76. COE 342 (T042) – Dr. Marwan Abu-Amara 76 Noise (1) Additional signals inserted between transmitter and receiver Thermal  Due to thermal agitation of electrons  Uniformly distributed  White noise Intermodulation  Signals that are the sum and difference of original frequencies sharing a medium

77. COE 342 (T042) – Dr. Marwan Abu-Amara 77 Noise (2) Crosstalk  A signal from one line is picked up by another Impulse  Irregular pulses or spikes  e.g. External electromagnetic interference  Short duration  High amplitude

78. COE 342 (T042) – Dr. Marwan Abu-Amara 78 More on Thermal (White) Noise Power of thermal noise present in a bandwidth B (Hz) is given by T is absolute temperature in kelvin and k is Boltzmann’s constant  k = 1.38  10 -23 J/K

79. COE 342 (T042) – Dr. Marwan Abu-Amara 79 Channel Capacity Data rate  In bits per second  Rate at which data can be communicated Bandwidth  In cycles per second of Hertz  Constrained by transmitter and medium

80. COE 342 (T042) – Dr. Marwan Abu-Amara 80 Nyquist Bandwidth If rate of signal transmission is 2B then signal with frequencies no greater than B is sufficient to carry signal rate Given bandwidth B, highest signal rate is 2B Given binary signal, data rate supported by B Hz is 2B bps Can be increased by using M signal levels C= 2B log 2 M

81. COE 342 (T042) – Dr. Marwan Abu-Amara 81 Shannon Capacity Formula Consider data rate,noise and error rate Faster data rate shortens each bit so burst of noise affects more bits  At given noise level, high data rate means higher error rate Signal to noise ratio (in decibels) SNR dB = 10 log 10 (signal/noise) Capacity C=B log 2 (1+SNR) This is error free capacity

82. COE 342 (T042) – Dr. Marwan Abu-Amara 82 E b /N 0 Determines digital data rates and error rates Standard quality measure for digital communication system performance Ratio of signal energy per bit to noise power density per Hertz E b = energy per bit in a signal (Joules) = ST b, where S = signal power (Watts), T b = time required to send 1 bit (seconds)  R = bit rate = 1/ T b

83. COE 342 (T042) – Dr. Marwan Abu-Amara 83 E b /N 0 (Cont.) Bit error rate for digital data is a decreasing function of E b /N 0  Given E b /N 0 to achieve a desired error rate, parameters in formula above may be selected E b /N 0 does not depend on bandwidth (vs. SNR) N = N 0 B T 

84. COE 342 (T042) – Dr. Marwan Abu-Amara 84 E b /N 0 (Cont.) Shannon’s result can be rewritten as: Relates achievable spectral efficiency C/B to E b /N 0