NyquistGrenze

NyquistGrenze, also known as Nyquist frequency, is the highest frequency that can be accurately represented in a discrete-time signal sampled at a given rate. It equals half the sampling frequency: F_Nyquist = Fs/2.

When a continuous-time signal with bandwidth limited to Fmax is sampled at Fs, the sampling theorem requires Fs > 2*Fmax. The NyquistGrenze is the boundary between representable and potentially aliased parts of the spectrum. Frequencies above NyquistGrenze are indistinguishable from reflected frequencies below NyquistGrenze, causing aliasing unless they are removed by an anti-aliasing filter before sampling.

Example: With a sampling rate of 44.1 kHz, the NyquistGrenze is 22.05 kHz. Content above that will alias into lower frequencies if not filtered.

Applications: In digital audio, communications, instrumentation, and signal processing, the NyquistGrenze guides anti-aliasing filter design and sampling choices. It also informs spectrum analysis and digital filter design.

History and terminology: The concept is named after Harry Nyquist, whose work laid foundational results for sampling and bandwidth limits, later connected with the Shannon sampling theorem. In German-language texts, the term NyquistGrenze is commonly used to denote this frequency boundary.

See also: Nyquist frequency, Nyquist rate, sampling theorem, anti-aliasing filter.