Nyquist–Shannon_sampling_theorem

# Nyquist–Shannon sampling theorem  ## Microsims — p5.js ### Nyquist–Shannon sampling theorem (p5.js) · `fs ≥ 2B` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/LtHYb0kBB" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Nyquist–Shannon sampling theorem — p5.js microsim"></iframe> </div> *Sample above twice the highest frequency and the continuous signal can be reconstructed perfectly — the theorem the whole movement rests on.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/LtHYb0kBB) · movement *I · Sampling, quantization & data conversion* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Companding]] *(in tree)* - [[Convolution]] *(in tree)* - [[Data_compression]] *(in tree)* - [[Delta_modulation]] *(in tree)* - [[Detection_theory]] *(in tree)* - [[Differential_pulse-code_modulation]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). 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`Émile_Borel` > Signal Processing concept · part of the Signal Processing Portal · movement I · !73 計算 keisan.svg ## From the Real GENERATIVE library ![Animated: Nyquist–Shannon sampling theorem](https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Nyquist_sampling.gif/400px-Nyquist_sampling.gif) *Animated: Nyquist–Shannon sampling theorem — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Information room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Nyquist_sampling.gif).* > The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing. ([Wikipedia](https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem))  ## Media (PD/CC)  !Gif Library/Nyquist–Shannon sampling theorem/Nyquist sampling.gif *Nyquist_sampling.gif · CC0*  ## What it is The Nyquist–Shannon sampling theorem states that a continuous-time signal whose spectrum contains no frequencies above $B$ hertz (a band-limited signal) is completely determined by, and can be perfectly reconstructed from, samples taken at a rate strictly greater than $2B$ samples per second. ## How it works / why it matters The critical rate $2B$ is called the **Nyquist rate**, and half the sampling rate, $f_s/2$, is the **Nyquist frequency** — the highest frequency that a given sampling rate can represent unambiguously. If $f_s > 2B$, the periodic copies (images) of the signal's spectrum created by sampling do not overlap, so an ideal low-pass filter can isolate the original spectrum and reconstruction (via the sinc-interpolation / Whittaker–Shannon formula) is exact. If the rate is too low, the spectral images overlap and fold back, which is Aliasing. This theorem is the theoretical foundation that makes digital audio (e.g. 44.1 kHz capturing frequencies up to ~22 kHz) and all lossless [[Sampling_(signal_processing)|sampling]] possible. ## Signs & universals This concept instantiates the semiotic universals: sampling · frequency · spectrum · signal — it relates the sampling rate to the signal's frequency content and spectral bandwidth. ## Related Completes the movement I triad: it governs [[Sampling_(signal_processing)]] and, when violated, causes Aliasing. The band-limiting condition is stated in terms of the signal spectrum, best understood via the Fourier transform. --- Back to Signal Processing Portal · the room · Semiotic gateway   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*   *Connected to the Apex Spine:* Nyquist–Shannon sampling theorem → [[Sine_wave|Sine wave]] → [[Wind_wave|Wind wave]] — [[WT!Thury_Hydrodynamics_Compendium|Compendium]] section 34, *Waves and tides*.   **Microsim — three.js (Wikitube framework):** *Nyquist–Shannon sampling theorem* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/flight/Nyquist–Shannon_sampling_theorem.html" data-title="Nyquist–Shannon sampling theorem"></div> *Built from `MICROSIM_GUIDE/specs/variants/Nyquist–Shannon_sampling_theorem.json`; part of the [[Aviation]] · [[Avionics]] flight set.*   *Linked from the [[Avionics]] hub, section X20, Flight recorders.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem) : [Wikitube](https://en.wikitube.io/wiki/Nyquist–Shannon_sampling_theorem) ## Previous hub tags Tree parent: [[Information_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*