GATE ECE 2008 | Question: 72

Question

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

• A. $16 \mathrm{~dB}$
• B. $32 \mathrm{~dB}$
• C. $48 \mathrm{~dB}$
• D. $64 \mathrm{~dB}$

Answer 1

Signal to noise ratio,
$$
\left(\frac{S_{0}}{N_{0}}\right)_{\mathrm{dB}} \approx 6 n \mathrm{~dB}
$$
where, $n=$ number of bits per sample quantized
$$
\left(\frac{S_{0}}{N_{0}}\right)_{\mathrm{dB}} \approx 6 \times 8=48 \mathrm{~dB}
$$