The Nyquist criterion is a theorem in signal processing that establishes the minimum sampling rate required for perfect reconstruction of a continuous-time signal. It states that the sampling rate fs must satisfy fs > 2·fmax, where fmax is the highest frequency present in the signal. The value 2·fmax is the Nyquist rate. Below this rate, frequency components above fs/2 fold back (alias) into the baseband, making perfect reconstruction impossible. The criterion persists through formal proof in sampling theory and is enforced in all digital signal processing systems. [formal: criterium-samplingis | substrate: mind | horizon: a life | explicit: yes | epoch: 1.00]
Accepted ontology entry
nyquist-criterion
The Nyquist criterion is a theorem in signal processing that establishes the minimum sampling rate required for perfect reconstruction of a continuous-time signal. It states that the sampling rate fs must satisfy fs > 2·fmax, where fmax is…
Definition
Why it is in scope
A mathematical rule in signal processing: to perfectly reconstruct a continuous signal from samples, the sampling rate must exceed twice the signal's highest frequency component. Human-made theorem from sampling theory; built to persist as a formal constraint in information and signal theory.
Names and aliases
- nyquist-criterionen · CANONICAL
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- cmrcnskwp00wz13vzse49jqk2INSTANCE_OF →
The Nyquist criterion is a specific theorem in signal processing — a provable statement about sampling rates. 'A theorem' is the nearest kind. Law 11c acknowledges universality but does not bar the edge.
- cmrw0g7st02xt2ceiy2ihtwthDEPENDS_ON →
The Nyquist criterion is a mathematical rule specifically about sampling rates — fs > 2·f_max. Remove the concept of sampling and the criterion ceases to operate in any domain. Law 8 removal test passes.
- cmr9uz3vv00elhcxfruyltnd4SERVES →
The Nyquist criterion serves measurement: it ensures that sampled measurements faithfully represent the original signal without aliasing distortion. Remove the need for faithful measurement and the criterion loses its purpose. The criterion is designed for the sake of measurement integrity (Law 8d).
Relations to this entry
- cmspchura04rdjlssvam2ao1a← DEPENDS_ON
An anti-aliasing filter is designed with its cutoff frequency set at the Nyquist frequency (half the sampling rate). Remove the Nyquist criterion concept and the filter has no cutoff specification — it ceases to operate as an anti-aliasing device. The removal test passes: the filter's operational parameter comes directly from the Nyquist criterion.
Record identity
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- Aug 11, 2026, 11:25 PM UTC
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- 0ecd62b9eb09411799b8a07c04777f6c7956211991a555884f58333127c1d7fa