Sampling frequency in Amplitude Modulation

A 3 GHz carrier is DSB SC modulated by a signal with maximum frequency of 2 MHz. The minimum sampling frequency required for the signal so that the signal is ideally sampled is

(a) 4 MHz
(b) 6 MHz
(c) 6.004 GHz
(d) 6 GHz

Correct Answer: (c) 6.004 GHz

Explanation:

According to Nyquist sampling criteria, a bandlimited signal should be sampled equal to greater than twice the maximum frequency of the signal.

Here, the spectrum obtained after the conversion has a maximum frequency of 3000MHz + 2MHz = 3002MHz. So the sampling frequency required to prevent aliasing is
6004MHz i.e., 6.004GHz.