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2017년09월23일 77번

[정보통신 개론] 대역폭 W인 채널을 통해 잡음 N이 섞인 신호 S를 전송할 때, 샤논의 정리에 의한 채널용량(bps) 산출식은?

  • ① Wlog2(1＋S/N)
  • ② Wloge(S＋N)
  • ③ log2(W×N×S)
  • ④ loge(1＋W×N/S)
(정답률: 73%)

문제 해설

Shannon's theorem states that the channel capacity (C) in bits per second (bps) is equal to the channel bandwidth (W) multiplied by the logarithm of the signal-to-noise ratio (S/N) plus 1, where the logarithm is base 2. Mathematically, this can be expressed as:

C = Wlog2(1 + S/N)

The reason for this formula is that the channel capacity is limited by the amount of noise present in the channel. As the signal-to-noise ratio increases, more information can be transmitted through the channel, and the channel capacity increases. The logarithmic function is used because the relationship between the signal-to-noise ratio and the channel capacity is not linear, but rather logarithmic. The base 2 logarithm is used because digital signals are typically represented in binary form, and the base 2 logarithm is most appropriate for binary calculations.
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