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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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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.
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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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? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about 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? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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