Continuous-time RNN and Shannon sampling theorem

1. What does Shannon's sampling theorem state?
2. What does the Nyquist Shannon theorem indicate?
3. What is sampling theorem in signals and systems?
4. Who formalized the sampling theorem?

What does Shannon's sampling theorem state?

Shannon's Sampling theorem states that a digital waveform must be updated at least twice as fast as the bandwidth of the signal to be accurately generated. The same image that was used for the Nyquist example can be used to demonstrate Shannon's Sampling theorem.

What does the Nyquist Shannon theorem indicate?

Nyquist's theorem states that a periodic signal must be sampled at more than twice the highest frequency component of the signal. In practice, because of the finite time available, a sample rate somewhat higher than this is necessary.

What is sampling theorem in signals and systems?

The sampling theorem specifies the minimum-sampling rate at which a continuous-time signal needs to be uniformly sampled so that the original signal can be completely recovered or reconstructed by these samples alone. This is usually referred to as Shannon's sampling theorem in the literature.

Who formalized the sampling theorem?

The sampling theorem was implied by the work of Harry Nyquist in 1928, in which he showed that up to 2B independent pulse samples could be sent through a system of bandwidth B; but he did not explicitly consider the problem of sampling and reconstruction of continuous signals.