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A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is _______
    Correct answer is '7 to 7'. Can you explain this answer?
    Verified Answer
    A sinusoidal message signal is converted to a PCM signal using a unifo...
    For sinusoidal signal
    (SNR)Q in dB = 6.0 n + 1.75 
    Given required (SNR)Q = 40 dB
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    A sinusoidal message signal is converted to a PCM signal using a unifo...
    Explanation:

    • Uniform Quantizer: A quantizer is a device that maps a continuous range of input values to a finite range of output values. In a uniform quantizer, the range of input values is divided into equal intervals and each interval is assigned a unique output value.

    • SQNR: Signal-to-quantization noise ratio (SQNR) is the ratio of the power of the signal to the power of the quantization noise. It is expressed in decibels (dB).

    • Minimum number of bits: The minimum number of bits per sample required to achieve the desired SQNR can be calculated using the following formula:
      $$SQNR = 6.02N + 1.76dB$$
      where N is the number of bits per sample.

    • Given: SQNR = 40dB

    • Calculation: Substituting the given value of SQNR in the above formula, we get:
      $$40 = 6.02N + 1.76$$
      Solving for N, we get:
      $$N = \frac{40-1.76}{6.02}$$
      $$N \approx 6.73$$
      Rounding up to the nearest integer, we get:
      $$N = 7$$

    • Answer: The minimum number of bits per sample needed to achieve the desired SQNR is 7.

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    A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is _______Correct answer is '7 to 7'. Can you explain this answer?
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