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In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________
Correct answer is '0.33'. Can you explain this answer?
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In a Binary digital communication system, the threshold voltage of com...
Probability density function of f (z/0) is
When '0' is transmitted, it will be detected as '1' with probability
⇒
Average probability of error = 0.
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In a Binary digital communication system, the threshold voltage of com...
Threshold Voltage and Input Range
In a binary digital communication system, the threshold voltage of the comparator is x volts. When a '0' is transmitted, the voltage at the input of the comparator is uniformly distributed in the range of x-0.5 to x-0.25. When a '1' is transmitted, the voltage at the input of the comparator is uniformly distributed in the range of x-0.25 to x+0.5.
Probability of Error
The probability of error in the system can be calculated by considering the overlap between the voltage ranges for '0' and '1' transmission.
Calculating Overlap
To calculate the overlap, we need to determine the probability of a '0' being misinterpreted as a '1' and the probability of a '1' being misinterpreted as a '0'.
Probability of Misinterpreting '0' as '1'
To misinterpret a '0' as '1', the input voltage should be greater than x-0.25. Since the input voltage is uniformly distributed in the range of x-0.5 to x-0.25 for '0' transmission, the probability of misinterpretation is given by the ratio of the overlap between the '0' and '1' voltage ranges to the total range of '0' transmission.
Overlap between '0' and '1' voltage ranges = (x-0.25) - (x-0.5) = 0.25
Total range of '0' transmission = (x-0.25) - (x-0.5) = 0.25
Therefore, the probability of misinterpreting '0' as '1' is 0.25/0.25 = 1.
Probability of Misinterpreting '1' as '0'
To misinterpret a '1' as '0', the input voltage should be less than x+0.25. Since the input voltage is uniformly distributed in the range of x-0.25 to x+0.5 for '1' transmission, the probability of misinterpretation is given by the ratio of the overlap between the '0' and '1' voltage ranges to the total range of '1' transmission.
Overlap between '0' and '1' voltage ranges = (x+0.25) - (x+0.5) = -0.25
Total range of '1' transmission = (x+0.5) - (x-0.25) = 0.75
Therefore, the probability of misinterpreting '1' as '0' is -0.25/0.75 = -1/3.
Average Probability of Error
The average probability of error in the system can be calculated by taking the average of the probabilities of misinterpreting '0' as '1' and '1' as '0'.
Average probability of error = (1 + (-1/3))/2 = 0.33
Therefore, the correct answer is 0.33, indicating that on average, 33% of transmitted bits will be misinterpreted in this binary digital communication system.
In a binary digital communication system, the threshold voltage of the comparator is x volts. When a '0' is transmitted, the voltage at the input of the comparator is uniformly distributed in the range of x-0.5 to x-0.25. When a '1' is transmitted, the voltage at the input of the comparator is uniformly distributed in the range of x-0.25 to x+0.5.
Probability of Error
The probability of error in the system can be calculated by considering the overlap between the voltage ranges for '0' and '1' transmission.
Calculating Overlap
To calculate the overlap, we need to determine the probability of a '0' being misinterpreted as a '1' and the probability of a '1' being misinterpreted as a '0'.
Probability of Misinterpreting '0' as '1'
To misinterpret a '0' as '1', the input voltage should be greater than x-0.25. Since the input voltage is uniformly distributed in the range of x-0.5 to x-0.25 for '0' transmission, the probability of misinterpretation is given by the ratio of the overlap between the '0' and '1' voltage ranges to the total range of '0' transmission.
Overlap between '0' and '1' voltage ranges = (x-0.25) - (x-0.5) = 0.25
Total range of '0' transmission = (x-0.25) - (x-0.5) = 0.25
Therefore, the probability of misinterpreting '0' as '1' is 0.25/0.25 = 1.
Probability of Misinterpreting '1' as '0'
To misinterpret a '1' as '0', the input voltage should be less than x+0.25. Since the input voltage is uniformly distributed in the range of x-0.25 to x+0.5 for '1' transmission, the probability of misinterpretation is given by the ratio of the overlap between the '0' and '1' voltage ranges to the total range of '1' transmission.
Overlap between '0' and '1' voltage ranges = (x+0.25) - (x+0.5) = -0.25
Total range of '1' transmission = (x+0.5) - (x-0.25) = 0.75
Therefore, the probability of misinterpreting '1' as '0' is -0.25/0.75 = -1/3.
Average Probability of Error
The average probability of error in the system can be calculated by taking the average of the probabilities of misinterpreting '0' as '1' and '1' as '0'.
Average probability of error = (1 + (-1/3))/2 = 0.33
Therefore, the correct answer is 0.33, indicating that on average, 33% of transmitted bits will be misinterpreted in this binary digital communication system.
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In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer?
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In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer?.
In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a Binary digital communication system, the threshold voltage of comparator is 'x' volts and voltage at input of comparator is uniformly distributed in the range of x-0.5 to x+0.25 when '0' is transmitted and it is in the range x-0.25 to x+0.5 when bit '1' is transmitted, the average probability of error in the system is_____________Correct answer is '0.33'. Can you explain this answer?.
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