GATE EC 2024 Set 1 — Question 57
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Communications → Random Processes → Autocorrelation & PSD
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Question
Let be a random process, where amplitude and phase are independent of each other, and are uniformly distributed in the intervals and , respectively. is fed to an 8-bit uniform mid-rise type quantizer. Given that the autocorrelation of is , the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is __________.
Correct answer
45 to 45.3
Solution
1.Signal Power (): The power of a random process is given by its autocorrelation at .
W.2.Quantizer Range: The signal is . The amplitude is uniformly distributed in . The maximum possible value of is and the minimum is . Thus, the peak-to-peak range is V.
3.Step Size (): For an 8-bit quantizer, the number of levels .
V.4.Quantization Noise Power (): For a uniform quantizer, W.
5.SQNR Calculation:
.6.SQNR in dB:
dB.Rounding to two decimal places, we get 45.15 dB.Continue learning with Success Tracker
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