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A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40 dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________ . 
  • a)
    7
  • b)
    10
  • c)
    5
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A sinusoidal message signal is converted to a PCM signal using a unifo...
Concept:
SNR (Signal to Noise Ratio) for a sinusoidal message signal Quantized uniformly with ‘n’ bits in given by;  SNRAB = 6n + 1.8
Calculation: Given, SNR = 40 dB, required at the output;
So, 40 ≤  6n + 1.8
6n ≥  40 – 1.8
n ≥  6.366
So, the minimum number of bits per sample needed to achieve the derived SQNR is 7 bits 
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Community Answer
A sinusoidal message signal is converted to a PCM signal using a unifo...
Calculation of Minimum Number of Bits per Sample

Given:
Signal-to-quantization noise ratio (SQNR) = 40 dB

Formula:
SQNR = 6.02 * N + 1.76 dB, where N is the number of bits per sample

Calculation:
40 = 6.02 * N + 1.76
38.24 = 6.02 * N
N ≈ 6.35

Minimum number of bits per sample needed = 7
Therefore, the minimum number of bits per sample needed to achieve the desired SQNR of 40 dB is 7.
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A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40 dB. The minimum number of bits per sample needed to achieve the desired SQNR is __________ .a)7b)10c)5d)3Correct answer is option 'A'. Can you explain this answer?
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