Home › Previous year questions › GATE 2017 EC (EC2) › Question 33GATE 2017 EC (EC2) – Question 33 Communications · Digital Communications · 1 mark · Numerical answer
A sinusoidal message signal is converted to PCM using a uniform quantizer. The required signal-to-quantization-noise ratio at the quantizer output is 40 dB. The minimum number of bits per sample needed is ________.
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Show answer and explanation Correct answer: 7 to 7
Explanation For a full-scale sinusoid and uniform N-bit quantizer, the usual quantization model gives $SQNR\approx6.02N+1.76$ dB.
Meeting 40 dB requires $N\ge(40-1.76)/6.02=6.35\ldots$. Bit depth must be an integer and must meet or exceed the target, so round up.
The minimum is **7 bits per sample**. Six bits give only about 37.88 dB.
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