What does the sampling theorem state regarding continuous signals?

The sampling theorem, also known as the Nyquist-Shannon theorem, states that a continuous signal can be completely represented in its discrete form if it is sampled at a rate that is at least twice the highest frequency present in the signal. This means that as long as the sampling frequency meets or exceeds this threshold, all the necessary information contained within the continuous signal can be accurately captured and reproduced. The concept ensures that no information is lost during the sampling process, allowing for the original signal to be perfectly reconstructed from its samples, provided proper techniques are used for reconstruction.

This principle is fundamental in digital signal processing and audio engineering, highlighting the importance of appropriate sampling rates when converting analog signals to digital. Proper sampling not only preserves the integrity of the signal but also plays a crucial role in various applications, such as in communication systems, where accurate representation over digital mediums is essential.