# Discrete time and continuous time <!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside --> ## Microsims — p5.js ### Discrete time and continuous time (p5.js) · `n vs t` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/SgHs1GrNu" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Discrete time and continuous time — p5.js microsim"></iframe> </div> *The two clocks of signals — a sequence of instants versus a continuous flow — and how sampling bridges them.* **Open in the editor:** [&#9654; fork this sketch](https://editor.p5js.org/sciencenibber/sketches/SgHs1GrNu) · movement *IX · Foundations & the rest of the toolbox* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Analog_signal]] *(in tree)* - [[Detection_theory]] *(in tree)* - [[Digital_image_processing]] *(in tree)* - [[Digital_signal_processing]] *(in tree)* - [[Discrete_cosine_transform]] *(in tree)* - [[Estimation_theory]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.* <!-- MICROSIMGEN:END --> ## Links (Wikipedia order) <!-- injected from _registry/childlinks/Discrete_time_and_continuous_time.json (2026-07-30T02:09:12Z) --> `Advanced_z-transform` · `Aliasing` · [[Analog_signal]] · `Anti-aliasing_filter` · `Audio_signal_processing` · `Bernoulli_process` · `Bilinear_transform` · `Calendar_year` · `Connected_space` · `Constant-Q_transform` · `Continuous_function` · `Continuum_(set_theory)` · `Countable_set` · [[Detection_theory]] · [[Differential_equation]] · `Digital_data` · [[Digital_image_processing]] · [[Digital_signal_processing]] · `Discrete-time_Fourier_transform` · `Discrete_Fourier_transform` · `Discrete_calculus` · [[Discrete_cosine_transform]] · `Discrete_system` · `Discretization` · `Downsampling_(signal_processing)` · [[Estimation_theory]] · `Excess_demand_function` · `Gross_domestic_product` · `Impulse_invariance` · `Income` · `Infinitesimal` · `Infinity` · `Integer` · [[Integral_transform]] · [[Laplace_transform]] · `Logistic_map` · `Matched_Z-transform_method` · `Measurement` · `Natural_number` · `Nyquist_frequency` · `Nyquist_rate` · [[Nyquist–Shannon_sampling_theorem]] · `Oversampling` · `Parameter` · [[Physics]] · `Price` · `Quantity` · [[Quantization_(signal_processing)]] · `Real_number` · `Regression_analysis` · [[Sampling_(signal_processing)]] · `Scientific_theory` · [[Sequence]] · `Speech_processing` · `Starred_transform` · `Step_function` · `Time-scale_calculus` · [[Time_series]] · `Uncountable_set` · `Undersampling` · `Upsampling` · `Variable_(mathematics)` · [[Z-transform]] · `Zak_transform` > Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg <!-- RENDER-THUMB:START --> !480 *Rendered from the live microsim (▶ motion).* <!-- RENDER-THUMB:END --> ## See it next [![Continuous-time signal|200](Continuous-time_signal_thumb.png)](Continuous-time_signal) *→ Continuous-time signal* <!-- VISUAL-LINK:END --> --- Back to Signal Processing Portal · the room · Semiotic gateway ## What it is Discrete time and continuous time are the two ways of modeling how a signal or system varies with time: continuous time treats time as a real-valued continuum, while discrete time treats it as a sequence of distinct instants, usually equally spaced samples. ## How it works / why it matters A continuous-time signal is defined for every instant and described by functions of a real variable, whereas a discrete-time signal is defined only at integer sample indices and described by sequences. Sampling converts continuous time to discrete time, and under the Nyquist–Shannon condition the samples preserve all information; this distinction determines whether calculus-based tools (differential equations, Laplace transforms) or difference-equation and z-transform methods apply. ## Signs & universals Instantiates: - signal — the concepts classify signals by their time index - system — systems are analyzed as continuous- or discrete-time systems - measurement — sampling is a measurement mapping continuous time to discrete instants ## Related Continuous-time signal, Discrete-time signal, Continuous signal, [[Analog_signal]], Digital signal (signal processing), [[Time_domain]] <!-- VISUAL-LINK:START --> <!-- CRAFT-LINK:START g12 --> *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].* <!-- CRAFT-LINK:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time) : [Wikitube](https://en.wikitube.io/wiki/Discrete_time_and_continuous_time) ## Previous hub tags Tree parents: [[Control_theory]] · [[Dynamical_system]] · [[System_dynamics]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*