The sampling theorem (Nyquist-Shannon) is a stated result of mathematical analysis: a continuous-time signal bandlimited to B hertz is completely determined, and exactly reconstructible, by its samples taken at any rate exceeding 2B hertz (the Nyquist rate), via sinc interpolation. Parameters: (1) bandwidth B of the signal, (2) sampling rate fs in samples per second, (3) Nyquist rate 2B as the minimum alias-free sampling rate, (4) the reconstruction kernel (sinc / ideal lowpass interpolation). Persistence mechanism: proved by Fourier-analytic methods and sustained in DSP textbooks, engineering curricula, and analog-to-digital design practice, where the choice of sampling rate is a decision grounded in this theorem. [formal: theorema nyquist-shannon | substrate: mind | horizon: generations | explicit: yes | epoch: 0.02]
Accepted ontology entry
sampling-theorem
The sampling theorem (Nyquist-Shannon) is a stated result of mathematical analysis: a continuous-time signal bandlimited to B hertz is completely determined, and exactly reconstructible, by its samples taken at any rate exceeding 2B hertz…
Definition
Why it is in scope
A human-made mathematical theorem — a stated result with a proof, not a discovered natural object — made to persist as a canonical result in DSP and information theory, taught and relied on in every analog-to-digital design.
Names and aliases
- sampling-theoremen · CANONICAL
Relations from this entry
- signal-samplingDERIVED_FROM →
The sampling practice preceded the theorem: Nyquist's 1928 condition on pulse rate arose inside telephony sampling practice, and Shannon's 1949 formulation generalized it. The theorem formalizes and bounds the pre-existing practice — it 'fixes the minimum rate for lossless reconstruction' of the sampled signal. Law 7: Y (the practice) existed first and fed into X (the theorem that systematized it).
- cmrcnskwp00wz13vzse49jqk2INSTANCE_OF →
The sampling theorem (Nyquist-Shannon) is a specific mathematical theorem about reconstructing continuous functions from discrete samples. A competent speaker would call the sampling theorem a theorem.
- cmsps9i0v06eejlssqrjcqyviSERVES →
The sampling theorem (Nyquist-Shannon) establishes the conditions for perfect reconstruction of continuous signals from discrete samples and serves signal processing by providing the foundational principle for all digital signal processing — without it, the conversion from analog to digital would lack theoretical guarantees.
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No accepted relations in this direction.
Record identity
- Created
- Sep 1, 2026, 9:56 PM UTC
- Content hash
- 3fdf5bd1c7f9bcb4950d7dfd484d09c96c988e9fea6668dd0c2e888f64a9a5eb