Digital Data, Analog Signals.

• Digital data are transmitted via analog signals via a modem
• These devices perform the digital to analog and analog to digital conversion.
• A carrier signal is the basic wave (signal) for transmitting information in an analog system.
• I stole this one from this site which claims it is from "The Encyclopedia of Networking and Telecommunications"

  "A carrier signal is a specific frequency in an analog communication 
  channel that is modulated with an information-carrying signal. 
  Carrier signals are commonly used in AM, FM, and other radio 
  transmissions to differentiate among channels. When you turn a radio 
  dial, you are selecting a carrier frequency. The radio then amplifies
  the signal carried on the selected frequency. In AM (amplitude modulation),
  modulation changes the strength or amplitude of the carrier signal. 
  In FM (frequency modulation), the frequency of the carrier signal
  is modulated."
      

• Stallings tells us that the carrier signal is modified in (at least) one of three ways:
  • The amplitude is modified (ASK)
  • The frequency is modified (FSK)
  • The phase is modified (PSK)
• 
• Amplitude Shift Keying (ASK)
  • let f_c be the carrier frequency.
  • s(t) = A cos(2πf_ct) if b = 1, 0 otherwise.
  • Inefficient
  • But apparently used is some fiber media.
  • On voice grade lines, only works for up to 1200 bps.
• Frequency Shift Keying (FSK)
  • Uses two frequencies near the carrier frequency
  • s(t) = Acos(2πf₀t) for 0
  • s(t) = Acos(2πf₁t) for 1
  • Where f_c + f_o = f₁
  • and f_c - f_o = f₀
  • Stallings tells us that some modems achieve full duplex by
    • One end uses f_c = 1170hz +/- 100 hz.
    • The other end uses f_c = 2125hz +/- 100hz
    • There is little overlap in the signals thus little interference.
  • MFSK (multiple fsk) is a technique to encode multiple bits per symbol
    • 
    • In the above, f ₁ = 2, f₂ = 4, f₃ = 6 and f₄ = 8
    • f_i = f_c + (2i -1 -M)f_d
      • 1 ≤ i ≤ M
      • f_c carrier frequency
      • M the number of signal elements 2^L
      • L the number of bits.
      • f_d the difference between signals.
    • If T is the bit period (data rate = 1/T), the then signal is held for T_s = LT seconds.
    • This requires a bandwidth of 2Mf_d
    • And 2f_d must be at least 1/T_s
• PSK (Phase shift keying)
  • Alter the phase for different bits.
  • s(t) = Acos(2πf_ct) if b = 0
  • s(t) = Acos(2πf_ct+π) if b = 1
  • The second is really (-Acos(2πf_ct))
  • There is a differential phase shift keying where 1 is represented by reversing the phase and 0 maintains the current phase.
  • 
  • Quadrature PSK
    • Offset by π/2 not π
    • This can carry 2 bits at a time.
  • This can be carried on with even more phase shifts.
    • Stallings tells us that a 9600 bps modem at 2400 baud uses 12 phase angles and some amplitude shifts.
  • Of the three techniques discussed, PSK does better, and even better under
• Quadrature Amplitude Modulation (QAM)
  • Used in asymmetric DSL
  • This is a combination of ASK and PSK
  • Two copies of the carrier frequency are used, one shifted by π/2
  • ASK is used on each of the bits.
  • s(t) = d₁(t)cos(2πf_ct)+d₂(t)sin(2πf_ct);
  • 
  • Stallings states that
    • using 2 amplitudes yields 8 levels or 3 bits.
    • Using 4 amplitudes yields 16 levels or 4 bits.
    • But this has more potential for error due to noise and attenuation.