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A sinusoid massage signal m(t) is transmitted by binary PCM without compression. If the signalto-quantization-noise ratio is required to be at least 48dB, the minimum number of bits per sample will be
- a)8
- b)10
- c)12
- d)14
Correct answer is option 'A'. Can you explain this answer?
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A sinusoid massage signal m(t) is transmitted by binary PCM without co...
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Signal-to-Quantization-Noise Ratio (SQNR)
The Signal-to-Quantization-Noise Ratio (SQNR) is a measure of the quality of a digital signal after quantization. It indicates the ratio of the power of the signal to the power of the quantization noise. A higher SQNR value indicates better signal quality.
PCM Encoding
In Pulse Code Modulation (PCM), an analog signal is sampled, quantized, and encoded into a digital signal. The analog signal is sampled at regular intervals, and each sample is assigned a digital value based on its amplitude. The number of bits used to represent each sample determines the resolution and the quality of the digital signal.
Finding the Minimum Number of Bits per Sample
To find the minimum number of bits per sample required to achieve a certain SQNR, we can use the following formula:
SQNR (in dB) = 6.02 * N + 1.76
Where N is the number of bits per sample.
In this case, the required SQNR is at least 48 dB. Plugging this value into the formula, we can solve for N:
48 = 6.02 * N + 1.76
46.24 = 6.02 * N
N ≈ 7.68
Since the number of bits per sample must be an integer, we round up to the nearest whole number, which is 8.
Therefore, the minimum number of bits per sample required to achieve a SQNR of at least 48 dB is 8.
Answer
The correct answer is option 'A' (8 bits).
The Signal-to-Quantization-Noise Ratio (SQNR) is a measure of the quality of a digital signal after quantization. It indicates the ratio of the power of the signal to the power of the quantization noise. A higher SQNR value indicates better signal quality.
PCM Encoding
In Pulse Code Modulation (PCM), an analog signal is sampled, quantized, and encoded into a digital signal. The analog signal is sampled at regular intervals, and each sample is assigned a digital value based on its amplitude. The number of bits used to represent each sample determines the resolution and the quality of the digital signal.
Finding the Minimum Number of Bits per Sample
To find the minimum number of bits per sample required to achieve a certain SQNR, we can use the following formula:
SQNR (in dB) = 6.02 * N + 1.76
Where N is the number of bits per sample.
In this case, the required SQNR is at least 48 dB. Plugging this value into the formula, we can solve for N:
48 = 6.02 * N + 1.76
46.24 = 6.02 * N
N ≈ 7.68
Since the number of bits per sample must be an integer, we round up to the nearest whole number, which is 8.
Therefore, the minimum number of bits per sample required to achieve a SQNR of at least 48 dB is 8.
Answer
The correct answer is option 'A' (8 bits).
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