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07 lecture 07 lecture Presentation Transcript

  • Introduction to TelecommunicationM J KhanLecture 07
  • Menu• Frequency and frequency domain• Fourier Transform• Discrete Fourier Transform (DFT)• Signal Encoding Techniques• Bit Encoding Techniques
  • 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.
  • Time domain VS Frequency domain
  • Time domain VS Frequency domainA complete sine wave in the time domaincan be represented by one single spike inthe frequency domain.
  • 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
  • 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
  • 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
  • Fourier AnalysisFourier analysis is a tool that changes a timedomain signal to a frequency domain signaland vice versa.
  • 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.
  • Fourier TransformFourier Transform gives the frequencydomain of a non-periodic time domain signal.
  • 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
  • Inverse DFTIn similar fashion we can transformfrequency domain to time domain10/2)(1)(NsNstjesFNtf
  • ExampleLet]123543[)(tf10/2)()(NtNstjetfsFWe knowBy Applying we get]5.1962i1.0000-0205.1962i-1.0000-18[)(sF
  • Frequency AnalysisFor more visit the web linkhttp://www.fourier-series.com/fourierseries2/DFT_tutorial.html
  • Signal Encoding Techniques• Digital Data Analog Signal• Analog Data Analog Signal• Analog Data Digital Signal
  • Digital Data Analog Signal
  • Digital Data Analog Signals
  • Digital Data Analog Signals
  • Amplitude Shift Keying
  • Frequency Shift Keying
  • Phase Shift Keying
  • Phase Shift Keying
  • 4-PSK
  • 8-PSK
  • Quadrature amplitude modulation is acombination of ASK and PSK so that amaximum contrast between each signalunit (bit, dibit, tribit, and so on) isachieved.Note:
  • The 4-QAM and 8-QAM collections
  • Time domain for an 8-QAM signal
  • 16-QAM collections
  • Bit and baud
  • 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
  • Analog Data Analog SignalsAmplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)
  • Analog Data Analog Signal
  • Analog Data Analog Signal
  • Amplitude Modulation
  • Angle Modulation
  • Analog Data Digital Signal
  • Pulse Code Modulation
  • Pulse Code ModulationPCM involves following steps1. Sampling2. Quantization3. Coding
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Analog SignalTime (seconds)Levels
  • Nyquist Sampling Theorem
  • Nyquist SamplingTheoremFs = Fc/2
  • Nyquist SamplingTheoremFs = Fc/2
  • Nyquist SamplingTheoremFs = Fc
  • Nyquist SamplingTheoremFs = Fc
  • Nyquist SamplingTheoremFs = 1.5*Fc
  • Nyquist SamplingTheoremFs = 1.5*Fc
  • Nyquist SamplingTheoremFs = 2*Fc
  • Nyquist SamplingTheoremFs = 2*Fc
  • Nyquist SamplingTheoremFs = 4*Fc
  • Nyquist SamplingTheoremFs = 4*Fc
  • Nyquist SamplingTheoremFs = 6*Fc
  • Nyquist SamplingTheoremFs = 6*Fc
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18SamplingTime (seconds)Levels
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18QuantizationTime (seconds)Levels
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18After SamplingTime (seconds)Levels
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18After QuantizationTime (seconds)Levels
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18001101000111100010011010101110111011101010011000100001111000100010000110CodingTime (seconds)Levels
  • Delta Modulation
  • Pulse Code ModulationDelta Modulation involves followingsteps1. Step up or Step down2. Coding
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Analog SignalTime (seconds)Levels
  • 1514131211109876543210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Follow the DifferenceTime (seconds)Levels
  • 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
  • Bit Encoding
  • 1 0 1 0 1 1 0 01Unipolar NRZNRZ-Inverted(DifferentialEncoding)BipolarEncodingDifferentialManchesterEncodingPolar NRZManchesterEncoding