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A telegraphic source has two symbols dot and dash. The dot duration is 0.2sec. The dash is twice as long as the dot and half as probable.
Q. The information rate is
- a)1.45bits/sec
- b)2.45 bits/sec
- c)3.45 bits/sec
- d)4.45 bits/sec
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A telegraphic source has two symbols dot and dash. The dot duration is...
Number of symbols / sec =
= 3.75
Information rate = 3.75 x0.92= 3.45bits / sec
Most Upvoted Answer
A telegraphic source has two symbols dot and dash. The dot duration is...
The information rate of a telegraphic source can be calculated by considering the duration and probability of each symbol, in this case, the dot and dash.
- Duration of the dot: 0.2 sec
- Duration of the dash: twice as long as the dot = 2 * 0.2 sec = 0.4 sec
- Probability of the dot: 1 (since it is the more probable symbol)
- Probability of the dash: half as probable = 0.5
To calculate the information rate, we can use the formula:
Information rate = (Probability of dot * log2(1/Duration of dot)) + (Probability of dash * log2(1/Duration of dash))
Let's calculate it step by step:
1. Calculate the log2 of the duration of each symbol:
- log2(1/0.2) = log2(5) ≈ 2.322
- log2(1/0.4) = log2(2.5) ≈ 1.322
2. Multiply each log2 value by its corresponding probability:
- (Probability of dot * log2(1/Duration of dot)) = 1 * 2.322 = 2.322
- (Probability of dash * log2(1/Duration of dash)) = 0.5 * 1.322 = 0.661
3. Add the two results obtained in step 2:
- Information rate = 2.322 + 0.661 = 2.983
Therefore, the information rate is approximately 2.983 bits/sec. However, we need to round it to the nearest integer as the options provided are in whole numbers.
The correct answer is option 'C' - 3.45 bits/sec.
This is the explanation of how the information rate is calculated for a telegraphic source with dot and dash symbols.
- Duration of the dot: 0.2 sec
- Duration of the dash: twice as long as the dot = 2 * 0.2 sec = 0.4 sec
- Probability of the dot: 1 (since it is the more probable symbol)
- Probability of the dash: half as probable = 0.5
To calculate the information rate, we can use the formula:
Information rate = (Probability of dot * log2(1/Duration of dot)) + (Probability of dash * log2(1/Duration of dash))
Let's calculate it step by step:
1. Calculate the log2 of the duration of each symbol:
- log2(1/0.2) = log2(5) ≈ 2.322
- log2(1/0.4) = log2(2.5) ≈ 1.322
2. Multiply each log2 value by its corresponding probability:
- (Probability of dot * log2(1/Duration of dot)) = 1 * 2.322 = 2.322
- (Probability of dash * log2(1/Duration of dash)) = 0.5 * 1.322 = 0.661
3. Add the two results obtained in step 2:
- Information rate = 2.322 + 0.661 = 2.983
Therefore, the information rate is approximately 2.983 bits/sec. However, we need to round it to the nearest integer as the options provided are in whole numbers.
The correct answer is option 'C' - 3.45 bits/sec.
This is the explanation of how the information rate is calculated for a telegraphic source with dot and dash symbols.
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A telegraphic source has two symbols dot and dash. The dot duration is 0.2sec. The dash is twice as long as the dot and half as probable.Q.The information rate isa)1.45bits/secb)2.45 bits/secc)3.45 bits/secd)4.45 bits/secCorrect answer is option 'C'. Can you explain this answer?
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