GATE EC 2019 Set 1 — Question 56
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Communications → Analog Communications → AM Modulation & Demodulation
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Question
A voice signal is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal , where kHz. The AM signal is to be digitized and archived. This is done by first sampling at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using bits, where is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is ________ Mbps.
Correct answer
11.8 to 11.82
Solution
1.The voice signal has a frequency range of 5 kHz to 15 kHz. The maximum frequency component is kHz.
2.The AM signal is . The frequency components in are and .
3.The highest frequency in the AM signal is kHz kHz.
4.The Nyquist rate for a signal with maximum frequency is kHz.
5.Assuming "Nyquist frequency" in the question refers to the Nyquist rate, the sampling frequency is kHz kHz.
6.For a 256-level quantizer, the number of bits per sample is bits.
7.The bit rate bits/sec Mbps.
8.Rounding to 2 decimal places, we get 11.81 Mbps.
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