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A speech signal is sampled at 8 kHz and encoded in PCM format using 8-bit/sample PCM data is transmitted through a baseband channel via 4-level PAM. Minimum Bandwidth required for transmission is
1. 16 kHz
2. 8 kHz
3. 24 kHz
4. 10 kHz

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Correct Answer - Option 1 : 16 kHz

Concept:

Baseband communication is given.

Minimum Bandwidth will be required if transmission of data takes place using sinc pulses and the bandwidth is given by:

\(B{W_{{\rm{min}}}} = \frac{{{R_b}}}{{2{{\log }_2}M}}\) 

Where Rb = n  fs

n = number of bits used to represent samples

fs = sampling rate.

Calculation:

In the Question, it is asked about minimum Bandwidth. we will consider that the transmission of data is taking place through sinc pulses.

Given fs = 8 kHz

n = 8 bits/sample

M = 4

Rb = nfs

\({\left( {BW} \right)_{min}} = \frac{{{R_b}}}{{2{{\log }_2}M}}\) 

\(= \frac{{n\;{f_s}}}{{2{{\log }_2}M}} = \frac{{8 \times 8}}{{2{{\log }_2}4}}\) 

\(= \frac{{64}}{{2 \times 2}} = 16\;kHz\) 

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