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Question

A band limited message signal which is uniformly distributed in the range [- 5 V, + 5 V] is sampled at nyquist rate and quantized using constant step size. The quantized samples are encoded using an n-bit encoder. If the minimum signal to quantization noise ratio required is 31.8 dB. then the minimum value of 'n' required will be______.
  1. 6

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Solution

The correct option is A 6
Message signal is uniformly distributed,

So, Signal power, S=55x2fX(x)dx

=55110x2dx=253W


Quantization noise power, NQ=Δ212=(10/2n)212=100(12)(22n)W=(253)22nW

So, SQNR=SNQ=22n=6.02ndB

(6.02)n31.8

n5.282

nmin=6

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