An audio signal s(t) = 5cos (2000πt) is quantized using 10-bit PCM. What is the signal-to-quantization noise ratio?

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UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper
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  1. 3.57 × 106
  2. 2.57 × 106
  3. 1.57 × 106
  4. 0.57 × 106

Answer (Detailed Solution Below)

Option 3 : 1.57 × 106
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Detailed Solution

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Quantization:

  • Quantization is the process of assigning voltage levels to the samples, is called quantization.
  •  This quantization noise can be decreased by increasing the number of quantization levels, is called signal to quantization noise ratio.

Given that, 

\(s(t) = 5cos(200\pi t) \)

number of bits n =10.

\({s}\over{Nq} \)\({3}\over{2} \)\(\times\)22n

\({3}\over{2}\)\(\times\)22\(\times\)10

= 1.5 x 220

= 1.57 \(\times\)106

Here, option 3 is correct.

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