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What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?
- a)(0,Δ)
- b)(-Δ,0)
- c)(-Δ/2,Δ/2)
- d)None of the mentioned
Correct answer is option 'C'. Can you explain this answer?
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What is the range in which the quantization errors due to rounding off...
Explanation: The Quantization errors due to rounding off are uniformly distributed random variables in the range (-Δ/2,Δ/2) if Δ=2-b. This is one of the assumption that is made about the statistical properties of the quantization error.
Most Upvoted Answer
What is the range in which the quantization errors due to rounding off...
If we assume that the quantization errors due to rounding off are uniformly distributed random variables, then the range in which these errors can occur will be determined by the number of bits used for quantization.
Let's say we have a quantization system with N bits. Each bit can represent one of two possible values (0 or 1), so the total number of possible quantization levels is 2^N. The range of quantization errors will depend on the step size, which is determined by the difference between adjacent quantization levels.
If we have a full-scale range of values from a minimum value (min) to a maximum value (max), then the step size can be calculated as (max - min) / (2^N - 1). This is because we need to divide the full-scale range into (2^N - 1) intervals to accommodate the quantization levels.
The range of quantization errors will then be half of the step size, since the quantization error can occur in either direction from the ideal quantization level. Therefore, the range of quantization errors will be (max - min) / (2^N - 1) / 2.
In summary, the range in which the quantization errors due to rounding off are uniformly distributed as random variables is determined by the number of bits used for quantization and the full-scale range of values being quantized.
Let's say we have a quantization system with N bits. Each bit can represent one of two possible values (0 or 1), so the total number of possible quantization levels is 2^N. The range of quantization errors will depend on the step size, which is determined by the difference between adjacent quantization levels.
If we have a full-scale range of values from a minimum value (min) to a maximum value (max), then the step size can be calculated as (max - min) / (2^N - 1). This is because we need to divide the full-scale range into (2^N - 1) intervals to accommodate the quantization levels.
The range of quantization errors will then be half of the step size, since the quantization error can occur in either direction from the ideal quantization level. Therefore, the range of quantization errors will be (max - min) / (2^N - 1) / 2.
In summary, the range in which the quantization errors due to rounding off are uniformly distributed as random variables is determined by the number of bits used for quantization and the full-scale range of values being quantized.
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What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?a)(0,Δ)b)(-Δ,0)c)(-Δ/2,Δ/2)d)None of the mentionedCorrect answer is option 'C'. Can you explain this answer?
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