GATE EC 2008 Set 1 Q72 — Digital Communications

A speech signal, band limited to $4 \; \mathrm{kHz}$ and peak voltage varying between $+5 \mathrm{V}$ and $-5 \mathrm{V}$, is sampled at the Nyquist rate. Each sample is quantized and represented by $8$ bits.

Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is