GATE EC 2016 Set 3 — Question 32
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Communications → Information Theory → Information Measure & Entropy
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Question
An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities and . The information rate (bits/sec) of the message source is __________
Correct answer
360 to 363
Solution
1.Determine the sampling rate ():
The signal is bandlimited to Hz. The Nyquist sampling rate is defined as:2.Determine the probabilities of the message symbols:
There are four symbols with probabilities . We are given:3.Calculate the entropy ():
Entropy is the average information per symbol:Using :
4.Calculate the information rate ():
The information rate is the product of the sampling rate and the entropy:The value falls within the acceptable range of 360 to 363.
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