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GATE 2016 EC (EC3) – Question 32

Communications · Information Theory · 1 mark · Numerical answer

A 100 Hz bandlimited analogue baseband signal is sampled at the Nyquist rate. Samples are quantized into independent symbols with probabilities p1=p4=0.125 and p2=p3. The source information rate in bits/s is ________.

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Correct answer: 360 to 363

Explanation

Normalization gives $p_2=p_3=(1-0.25)/2=0.375$. Entropy per sample is
$$\begin{aligned}H={}&-2(0.125\log_2 0.125)\\&-2(0.375\log_2 0.375).\end{aligned}$$
This is 1.811278 bits/sample. Nyquist sampling uses 200 samples/s, so the information rate is **362.256 bits/s**, within the official 360–363 interval.

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