Summary: Telecommunicatie

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• 2 Week 2

• 2.1.1 Review questions

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• What is the meaning of the bandwidth of a baseband signal?

  The bandwidth of a signal is the range of frequencies it occupies. For a baseband signal the lowest frequency is 0 Hz, so the bandwidth equals the highest frequency component present.

• What is the approximate bandwidth of a telephone-quality voice signal?

  
  Telephone-quality voice occupies approximately 300 Hz to 3.4 kHz, giving a band-width of about 3.1 kHz. Human voice can extend as low as 80 Hz–100 Hz, but those frequencies are not required for intelligibility

• Why is modulation required to transmit a voice signal wirelessly? Why not transmit thebaseband signal directly?

  
  Multiplying the message by a high-frequency carrier shifts its spectrum to a higher centre frequency (shorter wavelength), giving several advantages:
  1. Practical antenna size: antenna length is proportional to wavelength. A carrier at 1 MHz (λ ≈ 300 m) requires a far smaller antenna than a baseband voice signal.
  2. Frequency-division multiplexing: multiple stations can share the channel using different carrier frequencies without mutual interference.
  3. Channel matching: some propagation media are better suited to signals in specific frequency bands

• What is the main advantage of conventional AM (with carrier) over DSB-SC?

  
  AM with carrier can be demodulated using a simple envelope detector (a diode, resistor, and capacitor), requiring no knowledge of the carrier phase at the receiver. DSB-SC requires a phase-synchronised local oscillator, which is more complex and expensive.

• List three disadvantages of conventional AM (DSB-FC).

  
  1. Poor power efficiency: a large fraction of transmitted power is in the carrier, which carries no information.
  2. Double bandwidth: like DSB-SC, the bandwidth is 2W rather than the
  minimum W achievable with SSB.
  3. Noise susceptibility: wasted carrier power means less of the transmitter power budget goes to the information-bearing sidebands, degrading the signal-to-noise ratio.

• For an AM signal, what is the name given to the outline of the peaks of the carrier waveform, and what shape does it have?

  
  It is called the envelope. It follows the shape of the modulating signal (for a message m(t) it traces the function Ac[1 + μ ˆm(t)], where ˆm(t) is the normalised message).

• What mathematical operation does an amplitude modulator perform?

  
  Multiplication. The modulated signal is s(t) = Ac[1 + μm(t)] cos(2πfct), which is the product of the (amplitude-modulated) carrier and the message.

• True or false? The spectrum of an ideal DSB-SC signal contains a component at the carrier frequency fc.

  
  False. In an ideal DSB-SC modulator the carrier is suppressed, so there is no spectral component at fc. (In practice, imperfect balance in a balanced modulator may allow small carrier leakage.)

• What is the condition on the modulation index for envelope detection to work without distortion? What happens if this condition is violated

  
  The condition is μ ≤ 1 (100% modulation). If μ > 1 the envelope goes negative during part of the cycle (over-modulation), and the envelope no longer faithfully reproduces the message, causing distortion. Over-modulation also widens the signal bandwidth due to clipping-induced harmonics, potentially causing interference to adjacent channels.

• How does the frequency spectrum of a single-sideband (SSB) signal compare with that of a DSB signal for the same message?

  
  SSB transmits only one sideband (upper or lower), so its bandwidth is half that of DSB:
  • DSB bandwidth: 2W
  • SSB bandwidth: W
  SSB is therefore twice as spectrally efficient and also requires only half the transmitterpower for the same effective information power