Nyquistbetingelse

The Nyquistbetingelse, also known as the Nyquist–Shannon sampling theorem, is a fundamental principle in signal processing and information theory. It establishes the conditions under which a continuous-time signal can be perfectly reconstructed from its samples. The theorem was formulated by Harry Nyquist in 1928 and later expanded by Claude Shannon in 1949.

The core idea of the Nyquistbetingelse is that to accurately reconstruct a continuous-time signal from its discrete samples, the sampling frequency must be at least twice the highest frequency component present in the signal. This minimum sampling frequency is referred to as the Nyquist rate. For example, if a signal contains frequencies up to 3 kHz, the sampling rate must be at least 6 kHz to avoid aliasing, where higher frequencies are misrepresented as lower frequencies in the sampled signal.

The theorem assumes an ideal, infinite-bandwidth system and that the signal is band-limited, meaning it contains no frequencies higher than a certain maximum. In practice, signals are often not perfectly band-limited, which can lead to challenges in achieving perfect reconstruction. Additionally, the theorem does not account for noise or practical limitations in measurement systems, such as finite precision and quantization errors.

The Nyquistbetingelse is widely applied in digital audio, telecommunications, and other fields where signals are converted from analog to digital form. It helps engineers determine appropriate sampling rates for various applications, ensuring that the digital representation retains the essential characteristics of the original analog signal. Violating the Nyquistbetingelse can result in aliasing, distortion, and loss of information, making it a critical consideration in signal processing design.