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Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.
Consider a 1-bit quantizer that maps positive samples to value α and others to value β . If a* and b* are the respective choices for α and β that minimize the mean square quantization error, then (α* - β*) = _____. (round off to two decimal places)
  • a)
    1.15
  • b)
    1.18
Correct answer is between '1.15,1.18'. Can you explain this answer?
Most Upvoted Answer
Consider a real valued source whose samples are independent and ident...
Given probability density function can be drawn as shown below,
As area under probability density function is 1.
Function fx(x) can defined as,
Given quantized values are,
For 0 ≤ x ≤ 1,
Mean square quantization error will be,
3(α*)2 = 3(1 - α*)2
(α*)2 = (1 - α*)2
(α*) = 1- α*
2α* =1
α* = 1/2 = 0.5
For -2 ≤ x ≤ 0 ,
Mean square quantization error will be,
∴ α*- β* = 0.5 + 0.66 =1.16
Hence, the correct answer is 1.16.
Free Test
Community Answer
Consider a real valued source whose samples are independent and ident...
Given probability density function can be drawn as shown below,
As area under probability density function is 1.
Function fx(x) can defined as,
Given quantized values are,
For 0 ≤ x ≤ 1,
Mean square quantization error will be,
3(α*)2 = 3(1 - α*)2
(α*)2 = (1 - α*)2
(α*) = 1- α*
2α* =1
α* = 1/2 = 0.5
For -2 ≤ x ≤ 0 ,
Mean square quantization error will be,
∴ α*- β* = 0.5 + 0.66 =1.16
Hence, the correct answer is 1.16.
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Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.Consider a 1-bit quantizer that maps positive samples to value α and others to value β . If a* and b* are the respective choices for α and β that minimize the mean square quantization error, then (α* - β*) = _____. (round off to two decimal places)a)1.15b)1.18Correct answer is between '1.15,1.18'. Can you explain this answer?
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