Answer:
(a) 1.003 MHz
(b) increase the signal-to-noise ratio
Explanation:
The relationship between channel capacity, bandwidth, and signal-to-noise ratio was described by Claude Shannon in the 1940s, based on previous work by Harry Nyquist and Ralph Hartley. The relationship is given by the formula ...
C = Blog₂(1 +S/N)
where C is the channel capacity (bits per second), B is the bandwidth (Hz), and S/N is the signal to noise power ratio.
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<h3>(a)</h3>
You want to find B for C=10^7 and 10·log(S/N) = 30. Solving for B, we find ...
B = C/log₂(1 +S/N)
B = 10^7/log₂(1 +10^(30/10)) = 10^7/log₂(1001) ≈ 1.003 MHz
The allocated bandwidth must be at least 1.003 MHz.
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<h3>(b)</h3>
Shannon's relation tells us the alternative to increasing bandwidth is increasing signal-to-noise ratio. If "sufficient" bandwidth is not available, the signal-to-noise ratio must be increased.
