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A sinusoidal signal with peak to peak amplitude of 1.536 volt 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 V
- c)12 x 10-6 V
- d)3.072 Volt
Correct answer is option 'C'. Can you explain this answer?
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Quantization is the process of approximating a continuous signal with a finite number of discrete levels. In this case, a sinusoidal signal with a peak-to-peak amplitude of 1.536 volts is being quantized into 128 levels using a mid-rise uniform quantizer. We need to determine the quantization noise power.
Mid-rise uniform quantization means that the quantization levels are equally spaced and the decision threshold for each level is located at the midpoint of the adjacent levels. In this case, there are 128 levels, so the quantization step size can be calculated as:
Quantization Step Size = (Peak-to-Peak Amplitude) / (Number of Levels)
= 1.536 volts / 128
= 0.012 volts
Now, we need to find the quantization error or quantization noise. The quantization error is the difference between the actual value of the analog signal and its quantized representation. For a sinusoidal signal, the quantization error can be calculated as:
Quantization Error = (Quantization Step Size) / sqrt(12)
= 0.012 volts / sqrt(12)
≈ 0.003461 volts
The quantization noise power can be calculated by squaring the quantization error and then taking the average value. Since the quantization error is a random variable, it is assumed to be uniformly distributed between -0.5 and +0.5 times the quantization step size. Therefore, the average power of the quantization noise can be calculated as:
Quantization Noise Power = (Quantization Error)^2 / 12
= (0.003461 volts)^2 / 12
≈ 12 x 10^-6 volts
Hence, the correct answer is option 'C', i.e., the quantization noise power is approximately 12 x 10^-6 volts.
Mid-rise uniform quantization means that the quantization levels are equally spaced and the decision threshold for each level is located at the midpoint of the adjacent levels. In this case, there are 128 levels, so the quantization step size can be calculated as:
Quantization Step Size = (Peak-to-Peak Amplitude) / (Number of Levels)
= 1.536 volts / 128
= 0.012 volts
Now, we need to find the quantization error or quantization noise. The quantization error is the difference between the actual value of the analog signal and its quantized representation. For a sinusoidal signal, the quantization error can be calculated as:
Quantization Error = (Quantization Step Size) / sqrt(12)
= 0.012 volts / sqrt(12)
≈ 0.003461 volts
The quantization noise power can be calculated by squaring the quantization error and then taking the average value. Since the quantization error is a random variable, it is assumed to be uniformly distributed between -0.5 and +0.5 times the quantization step size. Therefore, the average power of the quantization noise can be calculated as:
Quantization Noise Power = (Quantization Error)^2 / 12
= (0.003461 volts)^2 / 12
≈ 12 x 10^-6 volts
Hence, the correct answer is option 'C', i.e., the quantization noise power is approximately 12 x 10^-6 volts.
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A sinusoidal signal with peak to peak amplitude of 1.536 volt is quantized into 128 levels using a mid-rise uniform quantizer. The quantization noise power isa)0.768 Vb)48 x 10-6 Vc)12 x 10-6 Vd)3.072 VoltCorrect answer is option 'C'. Can you explain this answer?
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