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MENTAL MODEL · M4554

Nyquist Frequency

Nyquist Frequency
TechnicalHigh supportComputer Science
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

The Nyquist frequency is half of the sampling frequency of a discrete signal system, named after the Swedish-American engineer Harry Nyquist or the Nyquist-Shannon sampling theorem. The sampling theorem states that as long as the Nyquist frequency of a discrete system is higher than the highest frequency or bandwidth of the sampled signal, aliasing can be avoided. Theoretically, even if the Nyquist frequency is just greater than the signal bandwidth (but not equal), it is sufficient to reconstruct the original signal through sampling. However, the reconstruction process requires a low-pass or band-pass filter to remove all high-frequency components above the Nyquist frequency, while ensuring that the components below the Nyquist frequency in the original signal are not distorted, which is impossible to achieve. In practice, to ensure the performance of the anti-aliasing filter, components near the Nyquist frequency may be distorted during sampling and signal reconstruction. Therefore, in practical applications, the signal bandwidth cannot approach the Nyquist frequency indefinitely; the specific situation depends on the performance of the filter used. The human ear hears between 20 Hz and 20 kHz.

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The Nyquist frequency is half of the sampling frequency of a discrete signal system, named after the Swedish-American engineer Harry Nyquist or the Nyquist-Shannon sampling theorem. The sampling theorem states that as long as the Nyquist frequency of a discrete system is higher than the highest frequency or bandwidth of the sampled signal, aliasing can be avoided. Theoretically, even if the Nyquist frequency is just greater than the signal bandwidth (but not equal), it is sufficient to reconstruct the original signal through sampling.

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For a given sampling rate fs, the Nyquist frequency is fs/2, which is the highest signal frequency that can be reconstructed without aliasing. Components above it fold into low-frequency artifacts (aliasing). The mechanism is the 'half-frequency boundary' of the sampling rate.

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