Discussion
A 3000 Hz bandwidth noisy channel transmits bits with a signal to thermal noise ratio of 30 dB. What is the maximum data rate of the channel ?
Answer: A
Correct answer: 30 kbps
This is Shannon's limit again, with a signal-to-noise ratio of 30 dB, that is 1000:
\[ C = 3000\log_{2}(1001) \approx 30{,}000\ \text{bps} \]
Note that the answer does not depend on how many levels the signalling uses; Shannon's bound holds whatever the modulation.
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