What if Carrier Frequency is greater than Sampling Frequency?

In general, to reconstruct a signal accurately, the sampling frequency must be at least twice the carrier frequency. While the Nyquist theorem provides this minimum limit, a higher sampling rate is often used to improve signal resolution.

Nyquist Criteria tells us the sampling frequency must be at least twice the highest frequency component present in the signal.

If the baseband message signal is 3 KHz, the sampling frequency must be 6 KHz or above. However, in practical scenarios or simulations, we often keep it ten times more than the message signal for better visualization. 

Similarly, for a modulated signal, we should set the sampling frequency at least twice (and ideally ten times) the carrier frequency. Some simulation examples show what happens if the sampling frequency is less than, equal to, or greater than twice the carrier frequency.

1. If the Sampling Frequency is Greater than the Carrier frequency 

2. If the Sampling Frequency is Equal to the Carrier frequency

 

 

 

 

3. If the Sampling Frequency is less than the Carrier frequency

 

 

Conclusion

Sampling frequency indicates the total number of samples available in a 1-second duration. If the sampling frequency is greater than twice the carrier frequency, the signal can be represented and reconstructed completely. However, if the sampling frequency is less than twice the carrier frequency, aliasing occurs and you will lose the information in the signal.

 

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[1] What should be the relationship among the message, carrier, and sampling frequencies?