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An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

1. 1 bit/sec
2. 2 bits/sec
3. 3 bits/sec
4. 4 bits/sec

Correct answer: 4 bits/sec

Solution

Four equiprobable levels carry log2(4)=2 bits per sample. Transmitting 2 samples per second gives an information rate of 2*2 = 4 bits/sec, which is option 4 (index 3), not 2 bits/sec.

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