engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Information Theory Information Content of a Discrete Memoryless System
In a system, voice signals with maximum frequency component of 3.5 kHz are sampled at twice the Nyquist rate. The sampled signal is quantized into levels that produce N symbols {s0, s1, s2, … , sN-2, sN-1}. These symbols occur independently with probabilities:
\(\frac{1}{2},\;\frac{1}{4},\frac{1}{8}, \ldots ,\frac{1}{{{2^{N - 1}}}},\frac{1}{{{2^{N - 1}}}}\).
The entropy as a function of N and the information rate of the message source for N = 8 is:1
\(\frac{{{2^{N - 1}} - 1}}{{{2^{N - 2}}}}\) 27.78 Kbps
2
\(\frac{{{2^N} - 1}}{{{2^{N - 1}}}}\) 27.89 Kbps
3
\(\frac{{{2^{N - 1}} - 1}}{{{2^{N - 2}}}}\) 13.89 Kbps
4
\(\frac{{{2^N} - 1}}{{{2^{N - 1}}}}\) 13.95 Kbps