07 lecture

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07 lecture

  1. 1. Introduction to TelecommunicationM J KhanLecture 07
  2. 2. Menu• Frequency and frequency domain• Fourier Transform• Discrete Fourier Transform (DFT)• Signal Encoding Techniques• Bit Encoding Techniques
  3. 3. Frequency• Frequency is the rate of change with respectto time.• Change in a short span of time means highfrequency.• Change over a long span of time means lowfrequency.
  4. 4. Time domain VS Frequency domain
  5. 5. Time domain VS Frequency domainA complete sine wave in the time domaincan be represented by one single spike inthe frequency domain.
  6. 6. Time domain VS Frequency domain0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10-505100 10 20 30 40 50 60 70 80 90 1000123450 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10-50510
  7. 7. Time domain VS Frequency domain0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10-505100 10 20 30 40 50 60 70 80 90 100012345
  8. 8. Time domain VS Frequency domain0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10-505100 10 20 30 40 50 60 70 80 90 100012345
  9. 9. Fourier AnalysisFourier analysis is a tool that changes a timedomain signal to a frequency domain signaland vice versa.
  10. 10. Fourier SeriesEvery composite periodic signal can berepresented with a series of sine and cosinefunctions. The functions are integralharmonics of the fundamental frequency “f”of the composite signal. Using the series wecan decompose any periodic signal into itsharmonics.
  11. 11. Fourier TransformFourier Transform gives the frequencydomain of a non-periodic time domain signal.
  12. 12. Discrete Fourier Transform (DFT)We are living digital age where every signalis• Sampled• Of finite extentThe DFT is the sampled Fourier Transform.10/2)()(NtNstjetfsF
  13. 13. Inverse DFTIn similar fashion we can transformfrequency domain to time domain10/2)(1)(NsNstjesFNtf
  14. 14. ExampleLet]123543[)(tf10/2)()(NtNstjetfsFWe knowBy Applying we get]5.1962i1.0000-0205.1962i-1.0000-18[)(sF
  15. 15. Frequency AnalysisFor more visit the web linkhttp://www.fourier-series.com/fourierseries2/DFT_tutorial.html
  16. 16. Signal Encoding Techniques• Digital Data Analog Signal• Analog Data Analog Signal• Analog Data Digital Signal
  17. 17. Digital Data Analog Signal
  18. 18. Digital Data Analog Signals
  19. 19. Digital Data Analog Signals
  20. 20. Amplitude Shift Keying
  21. 21. Frequency Shift Keying
  22. 22. Phase Shift Keying
  23. 23. Phase Shift Keying
  24. 24. 4-PSK
  25. 25. 8-PSK
  26. 26. Quadrature amplitude modulation is acombination of ASK and PSK so that amaximum contrast between each signalunit (bit, dibit, tribit, and so on) isachieved.Note:
  27. 27. The 4-QAM and 8-QAM collections
  28. 28. Time domain for an 8-QAM signal
  29. 29. 16-QAM collections
  30. 30. Bit and baud
  31. 31. Bit and baud rate comparisonModulation Units Bits/Baud Baud rate Bit RateASK, FSK, 2-PSK Bit 1 N N4-PSK, 4-QAM Dibit 2 N 2N8-PSK, 8-QAM Tribit 3 N 3N16-QAM Quadbit 4 N 4N32-QAM Pentabit 5 N 5N64-QAM Hexabit 6 N 6N128-QAM Septabit 7 N 7N256-QAM Octabit 8 N 8N
  32. 32. Analog Data Analog SignalsAmplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)
  33. 33. Analog Data Analog Signal
  34. 34. Analog Data Analog Signal
  35. 35. Amplitude Modulation
  36. 36. Angle Modulation
  37. 37. Analog Data Digital Signal
  38. 38. Pulse Code Modulation
  39. 39. Pulse Code ModulationPCM involves following steps1. Sampling2. Quantization3. Coding
  40. 40. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Analog SignalTime (seconds)Levels
  41. 41. Nyquist Sampling Theorem
  42. 42. Nyquist SamplingTheoremFs = Fc/2
  43. 43. Nyquist SamplingTheoremFs = Fc/2
  44. 44. Nyquist SamplingTheoremFs = Fc
  45. 45. Nyquist SamplingTheoremFs = Fc
  46. 46. Nyquist SamplingTheoremFs = 1.5*Fc
  47. 47. Nyquist SamplingTheoremFs = 1.5*Fc
  48. 48. Nyquist SamplingTheoremFs = 2*Fc
  49. 49. Nyquist SamplingTheoremFs = 2*Fc
  50. 50. Nyquist SamplingTheoremFs = 4*Fc
  51. 51. Nyquist SamplingTheoremFs = 4*Fc
  52. 52. Nyquist SamplingTheoremFs = 6*Fc
  53. 53. Nyquist SamplingTheoremFs = 6*Fc
  54. 54. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18SamplingTime (seconds)Levels
  55. 55. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18QuantizationTime (seconds)Levels
  56. 56. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18After SamplingTime (seconds)Levels
  57. 57. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18After QuantizationTime (seconds)Levels
  58. 58. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18001101000111100010011010101110111011101010011000100001111000100010000110CodingTime (seconds)Levels
  59. 59. Delta Modulation
  60. 60. Pulse Code ModulationDelta Modulation involves followingsteps1. Step up or Step down2. Coding
  61. 61. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Analog SignalTime (seconds)Levels
  62. 62. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Follow the DifferenceTime (seconds)Levels
  63. 63. 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Coding1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0Time (seconds)Levels
  64. 64. Bit Encoding
  65. 65. 1 0 1 0 1 1 0 01Unipolar NRZNRZ-Inverted(DifferentialEncoding)BipolarEncodingDifferentialManchesterEncodingPolar NRZManchesterEncoding

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