**Nyquist frequency** - in digital signal processing, a frequency equal to half the sampling frequency . Named after Harry Nyquist .

It follows from Kotelnikov’s theorem that when sampling an analog signal, there will be no loss of information only if (spectral density) the highest frequency of the useful signal is equal to half or less than the sampling frequency (in the English literature, the term Nyquist frequency is used to mean half the sampling frequency). Otherwise, when restoring the analog signal, there will be an overlap of spectral “tails” (frequency swapping, frequency masking, aliasing ), and the shape of the reconstructed signal will be distorted. If the signal spectrum does not have components higher than the Nyquist frequency, then the signal can be (theoretically) sampled and then reconstructed without distortion. In fact, the “digitization” of a signal (converting an analog signal to a digital one) is associated with quantization of samples - each sample is recorded as a digital code of finite bit depth, as a result of which quantization (rounding) errors are added to the samples, under certain conditions considered as “quantization noise”.

Real signals of finite duration always have an infinitely wide spectrum, more or less rapidly decreasing with increasing frequency. Therefore, the sampling of signals always leads to loss of information (distortion of the waveform during sampling — reconstruction), no matter how high the sampling frequency. At the selected sampling frequency, the distortion can be reduced by suppressing the spectral components of the analog signal (before sampling) lying above the Nyquist frequency, which requires a very high order anti-exchange filter to avoid overlapping “tails”. The practical implementation of such a filter is very difficult, since the amplitude-frequency characteristics of the filters are not rectangular, but smooth, and some transitional frequency band is formed between the passband and the suppression band. Therefore, the sampling frequency is chosen with a margin, for example, audio CDs use a sampling frequency of 44,100 Hertz , while the highest frequency in the spectrum of sound signals that a person can hear is considered to be 20,000 Hz. The Nyquist frequency margin of 44100/2 - 20,000 = 2050 Hz allows you to avoid frequency swapping when using a low-order filter.

## Links

- H. Nyquist, "Certain topics in telegraph transmission theory," Trans. AIEE, vol. 47, pp. 617–644, Apr. 1928