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Chapter 3: Data Transmission

COE 341: Data & Computer Communications (T061) Dr. Radwan E. Abdel-Aal. Chapter 3: Data Transmission. Remaining Six Chapters:. Chapter 7: Data Link: Flow and Error control, Link management. Data Link. Chapter 8: Improved utilization: Multiplexing. Physical Layer.

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Chapter 3: Data Transmission

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  1. COE 341: Data & Computer Communications (T061)Dr. Radwan E. Abdel-Aal Chapter 3: Data Transmission

  2. Remaining Six Chapters: Chapter 7: Data Link: Flow and Error control, Link management Data Link Chapter 8: Improved utilization: Multiplexing Physical Layer Chapter 6: Data Communication: Synchronization, Error detection and correction Chapter 4: Transmission Media Transmission Medium Chapter 5: Encoding: From data to signals Chapter 3: Signals, their representations, their transmission over media, Resulting impairments

  3. Agenda • Concepts & Terminology • Signal representation: Time and Frequency domains • Bandwidth and data rate • Decibels and Signal Strength (Appendix 3A ) • Fourier Analysis (Appendix B ) • Analog & Digital Data Transmission • Transmission Impairments • Channel Capacity

  4. Terminology (1) Transmission system: • Transmitter • Receiver • Transmission Media • Guided media • e.g. twisted pair, coaxial cable, optical fiber • Unguided media • e.g. air, water, vacuum

  5. Terminology (2) Link Configurations: • Direct link • Nointermediate ‘communication’ devices (these exclude repeaters/amplifiers) Two types: • Point-to-point • Only 2 devices share link • Multi-point • More than two devices share the same link, e.g. Ethernet bus segment A Amplifier C B

  6. Terminology (3) Transmission Types (ANSI Definitions) • Simplex • In one direction only all the time e.g. Television, Radio broadcasting • Duplex • In both directions • Two types: • Half duplex • Only one direction at a time e.g. Walki-Talki • Full duplex • In both directions at the same time e.g. telephone

  7. Frequency, Spectrum and Bandwidth • Time domain concepts • Analog signal • Varies in a smooth, continuous way in both time and amplitude • Digital signal • Maintains a constant level for sometime and then changes to another constant level (i.e. amplitude takes only a finite number of discrete levels) • Periodic signal • Same pattern repeated over time • Aperiodic signal • Pattern not repeated over time

  8. Analogue & Digital Signals

  9. T PeriodicSignals Temporal Period … t t+1T t+2T S (t+nT) = S (t); 0  t T Where: t is time over first period T is the waveform period n is an integer Signal behavior over one period describes behavior at all times

  10. Aperiodic (non periodic) Signals in time s(t) 1 0 t + X/2 - X/2

  11. T Sine Wave s(t) = A sin(2ft +) = A sin (F) A • Peak Amplitude (A) • Peak strength of signal, volts • T = Period = time for one repetition (cycle) • Repetition Frequency (f) • Measure of signal variations with time • In Hertz (Hz) (cycles per second) • f = 1/T(sec) = Hz • Angular Frequency (w) w = radians per second = 2 f = 2 /T • Phase () • Relative position in time, radians (how to determine?)

  12. Varying one of the three parameters of a sine wave carriers(t) = A sin(2ft +) = A sin(wt+F) Can be used to convey information…! M o d u l a t I o n Varying A Varying  Varying f

  13. Traveling Sine Waves(t) = A sin (k x -  t]  = Angular Frequency = 2 f = 2 / T Spatial Period = Wavelength k = Wave Number = 2 /   • For point p on the wave: • Total phase at t = 0: kx -  (0) = kx • Total phase at t = t: k(x+ x) -  (t) • Same total phase, • kx = k(x+ x) -  (t) • k x =  t Wave propagation velocity v = x / t v = /k = /T = f x p x Distance, x t = 0 t = t Direction of Wave Travel, Velocity v What is the expression for a wave traveling in the negative x direction? V is constant for a given wave type and medium v = f

  14. Wave Propagation Velocity, v m/s • Constant for a given wave type (e.g. electromagnetic, seismic, sound, ...) and propagation medium (air, water) • For all types of waves: • v = l f • For a given wave type (given v), higher frequencies correspond to shorter wavelengths and vise versa: Radio: long wave (km), short waves, … light (nm), etc.. • For electromagnetic waves: • In free space, v  speed of light in vacuum = c = 3x108 m/sec • Over other guided media v is lower than c

  15. Wavelength, l (meters) • Is the Spatial period of the wave: i.e. distance between two points in space where the wave has the same total phase • Also: Distance traveled by the wave during one temporal (time) cycle: dT = v T = (l f) T = l

  16. Continuous and Discrete Representations Availability of the signal over the horizontal axis (Time or Frequency) Continuous: Signal is defined at all points on the horizontal axis Sampling with a train of delta function Discrete: Signal is defined Only at certain points on the horizontal axis

  17. Frequency Domain Concepts • System response to sine waves is easy to analyze • Signals we deal with in practice are not all sine waves, e.g. Square waves • Can we relate practical waves to sine waves? YES • Fourier analysis shows that any signal can be treated as the sum of many sine wave components having different frequencies, amplitudes, and phases(Fourier Analysis: Appendix B) • This forms the basis for frequency domainanalysis • For a linear system, its response to a complex signal will be the sum of its response to the individual sine wave components of the signal. • Dealing with functions in the frequency domain is simpler than in the time domain

  18. Fundamental Addition of Twofrequency Components A = 1*(4/) frequency = f + 3rd harmonic A = (1/3)*(4/) frequency = 3f Frequency Spectrum = Approaching a square wave Fourier Series 3 t f Frequency Domain: S(f) vs f Time Domain: s(t) vs t Discrete Function in f Periodic function in t

  19. Asymptotically approaching a square wave by combining the fundamental + an infinite number of odd harmonics at prescribed amplitudes Topic of a programming assignment What is the highest Harmonic added?

  20. s(t) 1 0 t + X/2 - X/2 time More Frequency Domain Representations: A single square pulse (Aperiodic signal) Fourier Transform frequency 1/X Frequency Domain: S(f) vs f Time Domain: s(t) vs t Continuous Function in f Aperiodic function in t • What happens to the spectrum as the pulse gets broader …-> DC ? • What happens to the spectrum as the pulse gets narrower …-> spike ?

  21. Spectrum & Bandwidth • Spectrum • range of frequencies contained in a signal • Absolute (theoretical) Bandwidth (BW) • Is the width of spectrum = fmax- fmin • In many situations fmax =  • Effective Bandwidth • Often just bandwidth • Narrow band of frequencies containing most of the signal energy • Somewhat arbitrary: what is “most”? • DC Component • Component at zero frequency S(f) 7f 5f f 3f f

  22. Signal with a DC Component + _ t + 1V DC Level + t 1V DC Component

  23. = (fmax- fmin) Bandwidth for these signals:

  24. Received Waveform Limiting Effect of System Bandwidth 1,3 Better waveforms require larger BW BW = 2f More difficult reception with smaller BW f 3f 1 1,3,5 BW = 4f 5f f 3f 2 Varying System BW 1,3,5,7 BW = 6f 7f 5f f 3f 3 … BW =  1,3,5,7 ,9,… ……  7f 5f f 3f 4 Fourier Series for a Square Wave

  25. System Bandwidth and Achievable Data Rates • Any transmission system supports only a limitedband of frequencies(bandwidth) for satisfactory transmission • “system” includes: TX, RX, and Transmission medium • For example, this bandwidth is largest for optical fibers and smallest for twisted pair wires. • This limited system bandwidth degrades higher frequency components of the signal transmitted  poorer received waveforms  more difficult to interpret the signal at the receiver (especially with noise)  Data Errors • More degradation occurs when higher data rates are used (signal will have more components at higher frequency ) • This puts a limit on the data rate that can be used with agiven signal to noise requirement, receiver type, and a specified error performance  Channel capacity issues

  26. 5f f 3f Data Element = Signal Element Bandwidth and Data Rates Period T = 1/f T/2 Data rate = 1/(T/2) = 2/T bits per sec = 2f B 0 0 1 1 Data B = 4f Given a bandwidth B, Data rate = 2f = B/2 To double the data rate you need to double f: Two ways to do this… 1. Double the bandwidth with same received waveform(same RX conditions & error rate) 2B = 4f’ 2B 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 New bandwidth: 2B, Data rate = 2f’ = 2(2f)= 4f = B f’ 3f’ 5f’ 2. Same bandwidth, B, but tolerate poorer received waveform (needs better receiver, higher S/N ratio, or tolerating more errors in data) 1 B = 2f’ 0 0 0 1 1 1 0 B Bandwidth: B, Data rate = 2f’ = 2(2f) = 4f = B 5f’ 3f’ f’

  27. Bandwidth & Data Rates: Tradeoffs… Compromises • Increasing the data rate (bps) while keeping BWthe same means working with inferior (poorer) waveforms at the receiver, which may require: • Ensuring higher signal to noise ratio at RX (larger signal relative to noise): • Shorter link distances • Use of more en-route repeaters/amplifiers • Better shielding of cables to reduce noise, etc. • More sensitive (& costly!) receiver • Getting higher bit error rates • Tolerate them? • Add more efficient means for error detection and correction- this also increases overhead!.

  28. Appendix 3A: Decibels and Signal Strength • The decibel notation (dB) is a logarithmic measure of the ratio between two signal power levels • NdB= number of decibels • P1 = input power level • P2 = output power level • Example: • A signal with power level of 10mW is inserted into a transmission line • Measured power some distance away is 5mW • Power loss in dBs is expressed as NdB =10 log (5/10)=10(-0.3)= -3 dB • - ive dBs: P2 < P1 (Loss), • +ive dBs: P2 > P1 (Gain)

  29. Decibels and Signal Strength • Decibel notation is a relative, not absolute, measure: • A loss of 3 dB halves the power (could be 100 to 50, 16 to 8, …) • A gain of 3 dB doubles the power (could be 5 to 10, 7.5 to 15, …) • Will see shortly how we can handle absolute levels • Advantage: • The “log” allows replacing: • Multiplication with addition C = A * B Log C = Log A + Log B • and division with subtraction

  30. Amplifier ? 4 mW Gain: 35 dB Transmitted Signal Received Signal Loss: 10 dB Loss: 12 dB Decibels and Signal Strength • Example: Transmission line with an intermediate amplifier • Net power gain over transmission path: + 35 –12 – 10 =+13 dB (+ ive means there is actual net gain)  • Received signal power = (4 mW) log10-1(13/10) = 4 x 101.3 mW = 79.8 mW

  31. Relationship Between dB Values and Power ratio (P2/P1)

  32. WK 4 How to represent absolute power levels?Decibel-Watt (dBW) and Decibel-mW (dBm) • As a ratio relative to a fixed reference power level • Value of 1 W is a reference defined as 0 dBW • Value of 1 mW is a reference defined as 0 dBm • Examples: • Power of 1000 W is 30 dBW • –10 dBm represents a power of 0.1 mW Caution!: Must be same units at top and bottom Caution!: Must be same units at top and bottom X dBW = (X + ?) dBm

  33. Decibels and Signal Strength Everything in terms of dBs and dBm (or dBW) Levels  {dBs and dBms} can be added and subtracted. Same for {dBs and dBWs} • Example: Transmission line with an intermediate amplifier ? 4 mW Gain: 35 dB Transmitted Signal Received Signal Loss: 10 dB Loss: 12 dB Amplifier • Net power gain over transmission path: + 35 –12 – 10 =+13 dB (+ ive means actual net gain) TX Signal Power = 4 mW = 10 log (4/1) = 6.02 dBm • RX signal power (dBm) = 6.02 + 13 =19.02 dBm • Check: 19.02 dBm = 10 log (RX signal in mW/1 mW)  RX signal = log-1 (19.02/10) = 79.8 mW

  34. Decibels & Voltage ratios • Power decibels can also be expressed in terms of voltage ratios • Power P = V2/R, assuming same R • Decibel-millivolt (dBmV) is an absolute unit, with 0 dBmV being equivalent to 1mV. Note that this is still a power ratio… But expressed in voltages Caution!: Must be same units at top and bottom

  35. Appendix B: Fourier Analysis Signals in Time Aperiodic Periodic … Discrete Continuous Discrete Continuous DFS FS FT DFT Use Fourier Series Use Fourier Transform FS : Fourier Series DFS : Discrete Fourier Series FT : Fourier Transform DFT : Discrete Fourier Transform

  36. Fourier Series for periodic continuous signals • Any periodic signal x(t) of period T and repetition frequency f0 (f0 = 1/T) can be represented as an infinite sum of sinusoids of different frequencies and amplitudes – its Fourier Series. Expressed in Two forms: • 1. The sine/cosine form: Frequencies are multiples of the fundamental frequency f0 f0 = fundamental frequency = 1/T Where: DC Component = f(n) Two components at each frequency All integrals over one period only If A0 is not 0, x(t) has a DC component = f’(n)

  37. Fourier Series: 2. The Amplitude-Phase form: • Previous form had two components at each frequency (sine, cosine i.e. in quadrature) : An, Bn coefficients • The equivalent Amplitude-Phase representation has only one component at each frequency: Cn, qn • Derived from the previous form using trigonometry: cos (a) cos (b) - sin (a) sin (b) = cos [a +b] Now one component at each frequency nf0 Now components have different amplitudes, frequencies, and phases The C’s and ’s are obtained from the previous A’s and B’s using these equations. They are functions of n

  38. Fourier Series: General Observations

  39. Correction

  40. 1 -3/2 -1 -1/2 1/2 1 3/2 2 -1 T Fourier Series Example x(t) Note: (1) x(– t)=x(t)  x(t) is an even function (2) f0 = 1 / T = ½ Hz Note: A0 by definition is 2 x the DC content

  41. 1 -3/2 -1 -1/2 1/2 1 3/2 2 -1 T Contd… = 0 for n even = (4/n) sin (n/2) for n odd f0 =1/2 a function of n only Replacing t by –t in the first integral sin(-2pnf t)= - sin(2pnf t) Since x(– t)=x(t) as x(t) is an even function, then Bn = 0 for all n

  42. Contd… f0 = ½, so 2 f0 =  A0 = 0, Bn = 0 for all n, An = 0 for n even: 2, 4, … = (4/n) sin (n/2) for n odd: 1, 3, … Original x(t) is an even function! Amplitudes, n odd Cosine is an even function 3rd Harmonic 2 p 3 (1/2) t

  43. Another Example Previous Example x1(t) 1 -2 -1 1 2 -1 T Note that x1(-t)= -x1(t)  x(t) is an odd function Also, x1(t)=x(t-1/2) This waveform is the previous waveform shifted right by 1/2

  44. Another Example, Contd… Sine is an odd function As given before on slide 23. Because:

  45. Fourier Transform • For aperiodic (non-periodic) signal in time, the spectrum consists of a continuum of frequencies (not discrete components) • This spectrum is defined by the Fourier Transform • For a signal x(t) and a corresponding spectrum X(f), the following relations hold Imaginary nf0 f Inverse FT (from frequency to time ) Forward FT (from time to frequency) Real • X(f) is always complex (Has both real & Imaginary parts), even for x(t) real.

  46. (Continuous in Frequency) (non-periodic in time) Sinc function Sinc2 function

  47. Fourier Transform Example x(t) A Sin (x) / x i.e. “sinc” function

  48. A = A t f  1/ Fourier Transform Example, contd. Sin (x) / x “sinc” function Lim x0 (sin x)/x = (cos x)x=0/1 =1 Study the effect of the pulse width 

  49. The narrower a function is in one domain, the wider its transform is in the other domain The Extreme Cases

  50. Power Spectral Density (PSD) & Bandwidth • Absolute bandwidth of any time-limited signal is infinite • But luckily, most of the signal power will be concentrated in a finite band of lower frequencies • Power spectral density (PSD) describes the distribution of the power content of a signal as a function of frequency • Effective bandwidth is the width of the spectrum portion containing most of the total signal power • We estimate the total signal power in the time domain

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