GATE EC 2022 Set 1 — Question 64
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Communications → Probability → Expectation & Variance
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Question
Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, , as shown in the figure.
Consider a 1 bit quantizer that maps positive samples to value and others to value . If and are the respective choices for and that minimize the mean square quantization error, then (\alpha^* - \beta^*) = \text{_________} (rounded off to two decimal places).
Correct answer
1.15 to 1.18
Solution
The mean square quantization error is minimized when the representation levels and are the centroids of their respective quantization regions.
1.Determine the height of the PDF :
The total area under the PDF must be 1.2.Define the PDF :
- For , is a line from to : .
- For , .
- For , the centroid is:
- For , the centroid is:
4.Calculate the final result:
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