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A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization-noise power is
  • a)
    0.768 V
  • b)
    48 x 10-6 V2
  • c)
    12 x 10-6 V2
  • d)
    3.072 V
Correct answer is option 'C'. Can you explain this answer?
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A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantize...
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A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantize...
Quantization-Noise Power Calculation

Given Parameters
- Peak-to-peak amplitude of sinusoidal signal = 1.536 V
- Number of quantization levels = 128
- Quantizer type = mid-rise uniform

Mid-rise Uniform Quantizer
- In a mid-rise uniform quantizer, the quantization levels are centered on the mid-point between two consecutive steps.
- The quantization step size (Δ) can be calculated as:
Δ = (Peak-to-peak amplitude) / (Number of levels - 1)
Δ = 1.536 / 127
Δ = 0.012096 V

Quantization-Noise Power Calculation
- The quantization error is the difference between the actual signal value and the quantized value.
- For a sinusoidal signal, the quantization error is uniformly distributed between -Δ/2 and Δ/2.
- The power of the quantization error can be calculated as the variance of the uniform distribution.
- The variance of a uniform distribution between -a and a is given by:
Var = (a^2) / 3
- In this case, a = Δ/2 = 0.006048 V
- Therefore, the quantization-noise power is given by:
Power = Var = (a^2) / 3
Power = (0.006048^2) / 3
Power = 12 x 10^-6 V^2

Therefore, the correct answer is option C, which is 12 x 10^-6 V^2.
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A sinusoidal signal with peak-to-peak amplitude of 1.536 V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization-noise power isa)0.768 Vb)48 x 10-6V2c)12 x 10-6V2d)3.072 VCorrect answer is option 'C'. Can you explain this answer?
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