A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal is to be ideally sampled. The minimum frequency of the sampling impulse train should be

A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal is to be ideally sampled. The minimum frequency of the sampling impulse train should be Correct Answer 8 MHz

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Assertion (A): Nyquist rate of sampling is the theoretical minimum sampling rate at which the signal can be sampled and still be reconstructed from its samples. Reason (R): When the Nyquist rate sampling is used, only an ideal low pass filter can be used to extract signal x(t) from sampled signal xs(t). Code:
The signal $$\cos \left( {10\pi t + \frac{\pi }{4}} \right)$$   is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response $$\left( {\frac{{\sin \left( {\pi t} \right)}}{{\pi \tau }}} \right)\cos \left( {40\pi t - \frac{\pi }{2}} \right).$$     The filter output is