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It is assumed that quantization error, e(n) is a sequence of random variables where 1. The statistics do not change with time. 2. It is a sequence of uncorrelated random variables. 3. It is uncorrelated with the quantizer input x(n). 4. The probability density function is uniformly distributed over the range of values of quantization error. Which of the above statements are correct?

It is assumed that quantization error, e(n) is a sequence of random variables where 1. The statistics do not change with time. 2. It is a sequence of uncorrelated random variables. 3. It is uncorrelated with the quantizer input x(n). 4. The probability density function is uniformly distributed over the range of values of quantization error. Which of the above statements are correct? Correct Answer 1, 2 and 4 only

  • Quantization error, e(n) is a sequence of random variables and when the correlation coefficient of a random variable is equal to zero then they are called uncorrelated random variables. (Statement 2 is correct)
  • The probability density function is uniformly distributed over the range of values of quantization error (Statement 4 is correct) This is as shown:

           
           [ alt="F1 S.B Madhu 16.11.19 D 30" src="//storage.googleapis.com/tb-img/production/19/11/F1_S.B_Madhu_16.11.19_D%2030.png" style="width: 192px; height: 127px;"> 

  • The statistics remain unchanged with a period of time. (Statement 1 is correct)
  •  Quantization error, e(n)  is always correlated with the quantizer input x(n) as it depends on the input of input at the sampling instant. (Statement 3 is incorrect)

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