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A communication channel having AWGN characteristics is operating in such a way that SNR >> 1. The bandwidth of signal being transmitted is B and capacity C1. Determine the capacity of channel if a signal with half the bandwidth is transmitted through the same channel with same quality.
- a)0.5C1 – 0.5B
- b)0.5C1 + 0.5B
- c)0.5C1
- d)C1 – 0.5B
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A communication channel having AWGN characteristics is operating in s...
To determine the capacity of a communication channel when a signal with half the bandwidth is transmitted, we need to understand the relationship between bandwidth and capacity.
1. Capacity of a communication channel:
The capacity of a communication channel can be determined using the Shannon capacity formula, which is given by:
C = B * log2(1 + SNR)
Where C is the capacity of the channel in bits per second, B is the bandwidth of the signal, and SNR is the signal-to-noise ratio.
2. Given information:
In the given scenario, it is mentioned that the communication channel has AWGN (Additive White Gaussian Noise) characteristics and that the SNR is much greater than 1 (SNR >> 1). The bandwidth of the signal being transmitted is B, and the capacity of the channel is C1.
3. Capacity of the channel with a signal of half the bandwidth:
When a signal with half the bandwidth is transmitted through the same channel with the same quality, the new bandwidth becomes B/2. We can calculate the capacity of this channel using the Shannon capacity formula as follows:
C' = (B/2) * log2(1 + SNR)
4. Comparing the capacities:
To determine the capacity of the channel in this scenario, we can subtract the capacity of the new channel from the capacity of the original channel:
C2 = C1 - C'
Substituting the values of C1 and C' obtained from the Shannon capacity formula, we have:
C2 = C1 - (B/2) * log2(1 + SNR)
Simplifying further, we get:
C2 = C1 - 0.5B * log2(1 + SNR)
5. Final answer:
From the above equation, we can see that the capacity of the channel when a signal with half the bandwidth is transmitted is equal to 0.5 times the capacity of the original channel (C1) minus 0.5 times the bandwidth of the original signal (B).
Therefore, the correct answer is option 'C': 0.5C1.
1. Capacity of a communication channel:
The capacity of a communication channel can be determined using the Shannon capacity formula, which is given by:
C = B * log2(1 + SNR)
Where C is the capacity of the channel in bits per second, B is the bandwidth of the signal, and SNR is the signal-to-noise ratio.
2. Given information:
In the given scenario, it is mentioned that the communication channel has AWGN (Additive White Gaussian Noise) characteristics and that the SNR is much greater than 1 (SNR >> 1). The bandwidth of the signal being transmitted is B, and the capacity of the channel is C1.
3. Capacity of the channel with a signal of half the bandwidth:
When a signal with half the bandwidth is transmitted through the same channel with the same quality, the new bandwidth becomes B/2. We can calculate the capacity of this channel using the Shannon capacity formula as follows:
C' = (B/2) * log2(1 + SNR)
4. Comparing the capacities:
To determine the capacity of the channel in this scenario, we can subtract the capacity of the new channel from the capacity of the original channel:
C2 = C1 - C'
Substituting the values of C1 and C' obtained from the Shannon capacity formula, we have:
C2 = C1 - (B/2) * log2(1 + SNR)
Simplifying further, we get:
C2 = C1 - 0.5B * log2(1 + SNR)
5. Final answer:
From the above equation, we can see that the capacity of the channel when a signal with half the bandwidth is transmitted is equal to 0.5 times the capacity of the original channel (C1) minus 0.5 times the bandwidth of the original signal (B).
Therefore, the correct answer is option 'C': 0.5C1.
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Community Answer
A communication channel having AWGN characteristics is operating in s...
Here same quality implies that SNR for transmitted signals is kept equal. We have a formula for channel capacity as
C1=B1log2(1+S/N)
Now, B2 = 0.5 × B1. SNR is same, thus C2 would be,
C2 = 0.5 * B1log2(1 + S/N) = 0.5 * C1
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A communication channel having AWGN characteristics is operating in such a way that SNR >> 1. The bandwidth of signal being transmitted is B and capacity C1. Determine the capacity of channel if a signal with half the bandwidth is transmitted through the same channel with same quality.a)0.5C1 – 0.5Bb)0.5C1 + 0.5Bc)0.5C1d)C1 – 0.5BCorrect answer is option 'C'. Can you explain this answer?
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