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A \( 10 \)-bit coder is used. Its signal-to-quantisation-noise ratio is about

  • A.48 dB
  • B.30 dB
  • C.62 dB
  • D.60 dB

Answer: C

Applying the standard result for a full-scale sinusoid:

\[ \begin{aligned} \mathrm{SNR} &= 6.02n + 1.76 \\ &= 60.2 + 1.76 \approx 62 \ \mathrm{dB} \end{aligned} \]

so about 62 dB. Sixty decibels drops the constant term, which is the usual approximation and close enough for most purposes. 48 dB corresponds to eight bits and 30 dB to five. The six-decibels-per-bit slope is the part worth remembering; the additive constant is a refinement. The parameter that varies and the parameter that does not are worth naming before any substitution is attempted.

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