- 2074 Asoj · 3+3 marks
Capacity for 3.1 kHz, SNR 0 dB
Short answer
With B = 3.1 kHz and SNR = 0 dB (S/N = 1), capacity C = B log2(2) = 3100 bps = 3.1 kbps. This shows even unity SNR can support error-free transmission up to the bandwidth rate.
Find the capacity of a channel for a signal with a bandwidth of 3.1 kHz and signal to noise ratio of 0 dB and comment on it.
Given: B = 3.1 kHz, SNR = 0 dB.
- S/N = 10^(0/10) = 1
- C = B log₂(1 + S/N) = 3100 × log₂(1 + 1) = 3100 × 1
Answer: C = 3100 bps = 3.1 kbps.
Comment
- SNR of 0 dB means signal power equals noise power. Even then, Shannon says data can be sent without error at up to 3.1 kbps, but only with very good error-correcting codes and a large delay.
- The capacity in bits per second equals the bandwidth in Hz (1 bit/s/Hz). To get a higher rate in such a channel, the SNR must be improved: a low SNR makes a very poor channel.
✓ Answer checked by Claude Opus 5.5 (high effort)
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