NyquistShannonAbtasttheorie

The Nyquist-Shannon sampling theorem is a fundamental principle in digital signal processing. It states that if a function contains no frequencies higher than f, then it can be uniquely determined from samples taken at a rate greater than 2f. This rate, 2f, is known as the Nyquist rate.

Essentially, the theorem provides a mathematical guarantee that a continuous analog signal can be perfectly reconstructed from its discrete samples, provided that the sampling frequency is high enough. If the sampling frequency is too low, higher frequencies in the original signal can be misrepresented as lower frequencies in the sampled version, a phenomenon called aliasing. Aliasing leads to irreversible distortion of the reconstructed signal.

The theorem has widespread applications in fields such as telecommunications, audio and video recording, and image processing. For instance, in digital audio, the theorem dictates the sampling rate used for CDs (44.1 kHz), which is sufficient to capture the full range of human hearing (typically up to 20 kHz). In digital imaging, the resolution and sampling rate of a camera are governed by similar principles to ensure accurate representation of visual information. The Nyquist-Shannon sampling theorem is therefore a cornerstone of modern digital technology, enabling the conversion of analog information into a digital format that can be stored, transmitted, and processed reliably.