Nyquistegyenlet

Nyquistegyenlet, also known as the Nyquist-Shannon sampling theorem, is a fundamental principle in digital signal processing. It states that to perfectly reconstruct a signal from its samples, the sampling frequency must be at least twice the highest frequency present in the signal. This minimum sampling rate is referred to as the Nyquist rate.

The theorem is named after Harry Nyquist and Claude Shannon, who independently developed and published its concepts. Nyquist's work in the 1920s focused on the transmission of information through telegraph lines, while Shannon's groundbreaking 1949 paper "Communication in the Presence of Noise" formally established the theorem and its implications for digital communication and information theory.

If a signal is sampled below its Nyquist rate, a phenomenon called aliasing occurs. Aliasing causes higher frequencies in the original signal to be misrepresented as lower frequencies in the sampled signal, leading to distortion and loss of information. Therefore, when digitizing analog signals, it is crucial to ensure that the sampling rate satisfies the Nyquist criterion.

The Nyquist-Shannon sampling theorem has wide-ranging applications in various fields, including audio and video recording, telecommunications, medical imaging, and scientific data acquisition. It forms the theoretical basis for converting continuous analog signals into discrete digital representations that can be processed, stored, and transmitted efficiently.