NyquistinShannonsin

NyquistinShannonsin is a term used to describe the fundamental principle governing the sampling of continuous-time signals to convert them into discrete-time signals without losing information. It is named after Harry Nyquist and Claude Shannon, who independently developed key aspects of this theory.

The core of NyquistinShannonsin is the Nyquist-Shannon sampling theorem. This theorem states that a band-limited signal, meaning a signal whose frequency components are all below a certain maximum frequency, can be perfectly reconstructed from its samples if the sampling rate is at least twice the maximum frequency. This minimum sampling rate is known as the Nyquist rate, and the frequency itself is the Nyquist frequency.

If the sampling rate is below the Nyquist rate, a phenomenon called aliasing occurs. Aliasing causes higher frequencies in the original signal to be indistinguishable from lower frequencies in the sampled signal, leading to distortion and loss of information. Therefore, to avoid aliasing and ensure accurate signal reconstruction, the sampling rate must be strictly greater than twice the highest frequency present in the signal.

In practice, a small margin is often added to the sampling rate to account for imperfections in filters used to remove frequencies above the desired band. NyquistinShannonsin is a cornerstone of digital signal processing, essential for applications ranging from digital audio and video to telecommunications and medical imaging.