Signal Encoding Techniques Reasons for Choosing Encoding

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					                                                              Reasons for Choosing Encoding
                                                               Digital data, digital signal
                                                                 Equipment less complex and expensive than
Signal Encoding Techniques                                       digital-to-analog modulation equipment
                                                               Analog data, digital signal
                                                                 Permits use of modern digital transmission and
                  Chapter 6                                      switching equipment

Reasons for Choosing Encoding
Techniques                                                    Signal Encoding Criteria
  Digital data, analog signal                                  What determines how successful a receiver will be
    Some transmission media will only propagate                in interpreting an incoming signal?
    analog signals                                               Signal-to-noise ratio
                                                                 Data rate
    E.g., optical fiber and unguided media
  Analog data, analog signal                                   An increase in data rate increases bit error rate
    Analog data in electrical form can be                      An increase in SNR decreases bit error rate
    transmitted easily and cheaply
                                                               An increase in bandwidth allows an increase in
    Done with voice transmission over voice-grade              data rate

Factors Used to Compare                                       Factors Used to Compare
Encoding Schemes                                              Encoding Schemes
  Signal spectrum                                              Signal interference and noise immunity
    With lack of high-frequency components, less                 Performance in the presence of noise
    bandwidth required                                         Cost and complexity
    With no dc component, ac coupling via transformer            The higher the signal rate to achieve a given data rate,
    possible                                                     the greater the cost
    Transfer function of a channel is worse near band edges
    Ease of determining beginning and end of each bit
Basic Encoding Techniques                                                 Basic Encoding Techniques
 Digital data to analog signal
   Amplitude-shift keying (ASK)
      Amplitude difference of carrier frequency
   Frequency-shift keying (FSK)
      Frequency difference near carrier frequency
   Phase-shift keying (PSK)
      Phase of carrier signal shifted

Amplitude-Shift Keying                                                    Amplitude-Shift Keying
 One binary digit represented by presence of                               Susceptible to sudden gain changes
 carrier, at constant amplitude
 Other binary digit represented by absence of
                                                                           Inefficient modulation technique
 carrier                                                                   On voice-grade lines, used up to 1200 bps
                    A cos(2πf c t )             binary 1
                                                                           Used to transmit digital data over optical
          s (t ) =                                                        fiber
                         0                      binary 0

      where the carrier signal is Acos(2πfct)

Binary Frequency-Shift Keying                                             Binary Frequency-Shift Keying
(BFSK)                                                                    (BFSK)
 Two binary digits represented by two different                            Less susceptible to error than ASK
 frequencies near the carrier frequency
                                                                           On voice-grade lines, used up to 1200bps
                                                                           Used for high-frequency (3 to 30 MHz)
                 A cos(2πf t )                                            radio transmission
                                               binary 1
       s (t ) =            1
                 A cos(2πf 2t )
                                                binary 0                   Can be used at higher frequencies on LANs
                                                                           that use coaxial cable
      where f1 and f2 are offset from carrier frequency fc by equal but
      opposite amounts
Multiple Frequency-Shift Keying                       Multiple Frequency-Shift Keying
(MFSK)                                                (MFSK)
 More than two frequencies are used                     To match data rate of input bit stream,
 More bandwidth efficient but more susceptible to       each output signal element is held for:
                                                                          Ts=LT seconds
         s i (t ) = A cos 2 π f i t       1≤ i ≤ M
                                                             where T is the bit period (data rate = 1/T)
                                                        So, one signal element encodes L bits
      f i = f c + (2i – 1 – M)f d
      f c = the carrier frequency
      f d = the difference frequency
      M = number of different signal elements = 2 L
      L = number of bits per signal element

Multiple Frequency-Shift Keying                       Multiple Frequency-Shift Keying
(MFSK)                                                (MFSK)
 Total bandwidth required
   Minimum frequency separation required
 Therefore, modulator requires a bandwidth

Phase-Shift Keying (PSK)                              Phase-Shift Keying (PSK)
 Two-level PSK (BPSK)                                  Differential PSK (DPSK)
   Uses two phases to represent binary digits            Phase shift with reference to previous bit
                                                           Binary 0 – signal burst of same phase as previous
               A cos(2πf c t )
                                   binary 1               signal burst
     s (t ) = 
               A cos(2πf c t + π ) binary 0               Binary 1 – signal burst of opposite phase to previous
                                                           signal burst
              A cos(2πf c t )
                                       binary 1
           = 
              − A cos(2πf c t )
                                       binary 0
Phase-Shift Keying (PSK)                               QPSK and OQPSK
 Four-level PSK (QPSK)
   Each element represents more than one bit
                                 π
                A cos 2πf c t + 
                                4

                A cos 2πf ct + 
                                  3π 

   s(t ) = 
                                  4 
                                 3π 
                A cos 2πf ct −        00
                                 4 
                                 π
                A cos  2π f c t −    10
                                  4

Phase-Shift Keying (PSK)                               Performance
  Multilevel PSK
                                                        Bandwidth of modulated signal (BT)
    Using multiple phase angles with each angle
    having more than one amplitude, multiple signals      ASK, PSK        BT=(1+r)R
    elements can be achieved
                                                          FSK             BT=2DF+(1+r)R
                     R    R
              D=       =
                     L log 2 M                              R = bit rate
                                                            0 < r < 1; related to how signal is filtered
       D = modulation rate, baud
                                                            DF = f2-fc=fc-f1
       R = data rate, bps
       M = number of different signal elements = 2L
       L = number of bits per signal element

Performance                                            Performance
 Bandwidth of modulated signal (BT)
                      1+ r        1+ r 
   MPSK         BT =               log M  R
                              R =        
                      L           2 
   MFSK               (1 + r )M 
                      log M  R
                BT =            
                           2    
     L = number of bits encoded per signal element
     M = number of different signal elements
                                 Quadrature Amplitude
Performance                      Modulation
                                  QAM is a combination of ASK and PSK
                                    Two different signals sent simultaneously on
                                    the same carrier frequency

                                      s (t ) = d1 (t ) cos 2πf c t + d 2 (t )sin 2πf c t

Quadrature Amplitude
Modulation                       Reasons for Analog Modulation
                                  Modulation of digital signals
                                    When only analog transmission facilities are
                                    available, digital to analog conversion required
                                  Modulation of analog signals
                                    A higher frequency may be needed for effective
                                    Modulation permits frequency division

Basic Encoding Techniques        Amplitude Modulation
 Analog data to analog signal     Amplitude Modulation
   Amplitude modulation (AM)
                                      s (t ) = [1 + n a x (t )]cos 2π f c t
   Angle modulation
     Frequency modulation (FM)        cos2πfct = carrier
     Phase modulation (PM)            x(t) = input signal
                                      na = modulation index
                                          Ratio of amplitude of input signal to carrier
                                    a.k.a double sideband transmitted carrier
Spectrum of AM signal                                     Amplitude Modulation
                                                           Transmitted power
                                                                              n 2
                                                                     Pt = Pc 1 + a 
                                                                                 2 
                                                               Pt = total transmitted power in s(t)
                                                               Pc = transmitted power in carrier

Single Sideband (SSB)                                     Angle Modulation
 Variant of AM is single sideband (SSB)                     Angle modulation
                                                                    s (t ) = Ac cos[2πf c t + φ (t )]
   Sends only one sideband
   Eliminates other sideband and carrier
                                                            Phase modulation
   Only half the bandwidth is required
   Less power is required                                     Phase is proportional to modulating signal
                                                                           φ (t ) = n p m(t )
   Suppressed carrier can’t be used for synchronization
   purposes                                                      np = phase modulation index

Angle Modulation                                          Angle Modulation
 Frequency modulation                                      Compared to AM, FM and PM result in a
   Derivative of the phase is proportional to              signal whose bandwidth:
   modulating signal                                         is also centered at fc
                                                             but has a magnitude that is much different
                 φ ' (t ) = n f m(t )                          Angle modulation includes cos(∅ (t)) which
                                                               produces a wide range of frequencies
      nf = frequency modulation index
                                                           Thus, FM and PM require greater
                                                           bandwidth than AM
Angle Modulation                                     Basic Encoding Techniques
 Carson’s rule                                        Analog data to digital signal
                                                        Pulse code modulation (PCM)
  where       BT = 2(β + 1)B                            Delta modulation (DM)
             n p Am         for PM
        β =  ∆F n f Am
             B  =           for FM
                   2πB
 The formula for FM becomes
                 BT = 2∆F + 2 B

Analog Data to Digital Signal                        Pulse Code Modulation
 Once analog data have been converted to              Based on the sampling theorem
 digital signals, the digital data:                   Each analog sample is assigned a binary
   can be transmitted using NRZ-L                     code
   can be encoded as a digital signal using a code      Analog samples are referred to as pulse
   other than NRZ-L                                     amplitude modulation (PAM) samples
   can be converted to an analog signal, using        The digital signal consists of block of n bits,
   previously discussed techniques                    where each n-bit number is the amplitude of
                                                      a PCM pulse

Pulse Code Modulation                                Pulse Code Modulation
                                                      By quantizing the PAM pulse, original
                                                      signal is only approximated
                                                      Leads to quantizing noise
                                                      Signal-to-noise ratio for quantizing noise
                                                       SNR dB = 20 log 2 n + 1.76 dB = 6.02n + 1.76 dB

                                                      Thus, each additional bit increases SNR by
                                                      6 dB, or a factor of 4
Delta Modulation                                    Delta Modulation
 Analog input is approximated by staircase
   Moves up or down by one quantization level
   (δ) at each sampling interval
 The bit stream approximates derivative of
 analog signal (rather than amplitude)
   1 is generated if function goes up
   0 otherwise

                                                    Reasons for Growth of Digital
Delta Modulation                                    Techniques
 Two important parameters                            Growth in popularity of digital techniques
   Size of step assigned to each binary digit (δ)    for sending analog data
   Sampling rate                                       Repeaters are used instead of amplifiers
 Accuracy improved by increasing sampling                No additive noise
 rate                                                  TDM is used instead of FDM
   However, this increases the data rate                 No intermodulation noise
 Advantage of DM over PCM is the                       Conversion to digital signaling allows use of
 simplicity of its implementation                      more efficient digital switching techniques

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