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Four messages band-limited to W, W, 2W, and 3W respectively ...

 

Four messages band-limited to W, W, 2W, and 3W respectively are to be multiplexed using Time Division Multiplexing (TDM).
The minimum bandwidth required for transmission of this TDM signal is:

Options:

  • (a) W

  • (b) 3W

  • (c) 6W

  • (d) 7W



Solution: Minimum Bandwidth for TDM

For a band-limited signal of bandwidth B, the minimum sampling rate required is 2B (Nyquist criterion).

Sampling rates of the four messages:

  • Bandwidth W → Sampling rate = 2W
  • Bandwidth W → Sampling rate = 2W
  • Bandwidth 2W → Sampling rate = 4W
  • Bandwidth 3W → Sampling rate = 6W

Total sampling rate: 2W + 2W + 4W + 6W = 14W

In TDM, the minimum required transmission bandwidth is half the total sampling rate:

Required Bandwidth = 14W / 2 = 7W

Correct Answer: (d) 7W

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