What does the Nyquist theorem state?

The Nyquist theorem, also known as the Nyquist-Shannon sampling theorem, fundamentally states that to accurately reconstruct a continuous signal from its samples, the sampling rate must be at least twice the highest frequency component present in that signal. This minimum sampling rate is referred to as the Nyquist rate. When this criterion is met, it ensures that no information is lost during the sampling process and that the original analog signal can be perfectly reconstructed from the sampled data.

This theorem is crucial in many fields, including telecommunications and digital signal processing, where signals need to be digitized for transmission or storage. Failure to adhere to this rule can lead to aliasing, where higher frequencies are misrepresented as lower frequencies, distorting the resulting signal. Thus, understanding the critical importance of sampling at or above the Nyquist rate is essential for any technology that relies on converting analog signals to digital formats.