The Nyquist-Shannon sampling theorem states that to reconstruct a signal, the sampling frequency ($f_s$) must be greater than twice its bandwidth ($B$). For a baseband signal (like voice), the bandwidth is the same as the highest frequency ($f_{max}$), so $f_s > 2f_{max}$.
For example, voice bandwidth is typically 300 Hz to 3.3 kHz. To simplify filtering, we treat the maximum frequency ($f_{max}$) as 4 kHz. By Nyquist, to prevent aliasing, the sampling frequency must be at least 8 kHz ($2 \times 4\,\mathrm{kHz}$).
When modulating a signal, the carrier frequency ($f_c$) should be significantly higher than the message bandwidth ($B$) to allow for efficient transmission and filtering.
In practical simulations (like MATLAB), if you want to see the actual shape of the carrier wave, the sampling frequency ($f_s$) must be at least twice the carrier frequency:
$$f_s > 2f_c$$
Practical Guidelines for Simulation:
- Set the carrier frequency ($f_c$) to be at least 10 times the message frequency ($f_m$).
- Set the sampling frequency ($f_s$) to be at least 10 times the carrier frequency ($f_c$).
This ensures that the Nyquist criterion is met for both the message and the carrier, preventing information loss and providing a smooth waveform for analysis.