A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with μ = 225.Que: The signal-to-quantization-noise ratio isa)34.91 dBb)38.06 dBc)42.05 dBd)48.76 dBCorrect answer is option 'B'. Can you explain this answer?

Question

A signal has a bandwidth of 1 MHz. It is sampled at a rate 50% higher than the Nyquist rate and quantized into 256 level using a -low quantizer with &#956; = 225.Que: The signal-to-quantization-noise ratio isa)34.91 dBb)38.06 dBc)42.05 dBd)48.76 dBCorrect answer is option 'B'. Can you explain this answer?

Answer

Given information:
Bandwidth of signal = 1 MHz
Sampling rate = 1.5 x Nyquist rate
Quantization levels = 256
Quantizer step size = 225

Calculation:
Nyquist rate = 2 x 1 MHz = 2 MHz
Sampling rate = 1.5 x 2 MHz = 3 MHz

1. Quantization noise power:
The quantization noise power can be calculated using the formula:
Q = (1/12) x ∆²
where Q is the quantization noise power and ∆ is the quantization step size.

Here, ∆ = 225
Q = (1/12) x 225² = 42187.5

2. Signal power:
The signal power can be calculated using the formula:
Psignal = (Bandwidth/2) x A²
where A is the amplitude of the signal.

Here, A is not given, but we can assume it to be 1, as it does not affect the SNR calculation.
Psignal = (1/2) x 1² = 0.5

3. Signal-to-quantization-noise ratio:
The signal-to-quantization-noise ratio (SNR) can be calculated using the formula:
SNR = 10log10(Psignal/Q)

SNR = 10log10(0.5/42187.5) = 38.06 dB

Therefore, the signal-to-quantization-noise ratio is 38.06 dB (option B).

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