Transfer_function - Wikiparency

# Transfer function  ## Microsims — p5.js ### Transfer function (p5.js) · `Y(s)/X(s)` <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/Ee-7lj8cw" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Transfer function — p5.js microsim"></iframe> </div> *The ratio of output to input in the transform domain — a system's behavior in one compact expression.* **Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/Ee-7lj8cw) · movement *VI · Control theory & estimation* · library `p5js` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Control_theory]] *(in tree)* - [[Convolution]] *(in tree)* - [[Frequency_domain]] *(in tree)* - [[Frequency_response]] *(in tree)* - [[Impulse_response]] *(in tree)* - [[Laplace_transform]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## Links (Wikipedia order)  `Actuator` · `Amplifier` · `Amplitude` · `Analog_computer` · [[Angular_frequency]] · `Argument_(complex_analysis)` · [[Black_box]] · [[Block_diagram]] · `Bode_plot` · `Butterworth_filter` · `Characteristic_equation_(calculus)` · `Chebyshev_filter` · [[Chemical_reaction_engineering]] · `Chemical_reactor` · `Communication_theory` · `Complex_number` · [[Control_engineering]] · [[Control_system]] · [[Control_theory]] · [[Convolution]] · `Describing_function` · [[Differential_equation]] · `Duhamel's_principle` · `Electronic_circuit_simulation` · `Electronic_filter` · `Elliptic_filter` · [[Engineering]] · `Filter_(signal_processing)` · `Fourier_transform` · `Frequency` · [[Frequency_domain]] · [[Frequency_response]] · `Function_(mathematics)` · `Garrett_Birkhoff` · `Harmonic` · `Howard_Harry_Rosenbrock` · `Imaging` · [[Impulse_response]] · `Integer` · [[Laplace_transform]] · `Linear_differential_equation` · [[Linear_time-invariant_system]] · `Luminous_intensity` · [[Mathematical_model]] · `Nonlinear_control` · `Operational_amplifier` · `Phase_(waves)` · `Photodetector` · `Point_spread_function` · `Proper_transfer_function` · `Relaxation_oscillator` · `Residence_time` · `Rosenbrock_system_matrix` · `Scalar_(mathematics)` · `Semi-log_plot` · [[Signal-flow_graph]] · [[Signal_processing]] · [[Sine_wave]] · `Spatial_frequency` · `State-space_representation` · `Transfer_function_matrix` · `Transfer_functions_in_imaging` · `Transformation_(function)` · `Transient_response` · `Wavelength` · [[Z-transform]] > Signal Processing concept · part of the Signal Processing Portal · movement VI · !01 制御 seigyo.svg  !480 *Rendered from the live microsim (▶ motion).*  ## See it next [![Linear time-invariant system|200](Linear_time-invariant_system_thumb.png)](Linear_time-invariant_system) *→ [[Linear_time-invariant_system|Linear time-invariant system]]*  --- Back to Signal Processing Portal · the room · Semiotic gateway ## What it is A transfer function is the ratio of the transform of a linear time-invariant system's output to the transform of its input (with zero initial conditions), compactly describing how the system reshapes every frequency it is given. ## How it works / why it matters Using the Laplace transform $H(s)=Y(s)/X(s)$ for continuous systems or the z-transform $H(z)$ for discrete ones, the transfer function turns convolution into multiplication and encodes the system's behavior in its poles and zeros: pole locations govern stability and resonance, and evaluating along the imaginary axis or unit circle gives the frequency response. This makes it the central tool for analyzing and designing filters and control loops — reading damping, bandwidth, and stability directly from the pole–zero map. ## Signs & universals Instantiates the semiotic universals: signal · stability · feedback. ## Related The algebraic signature of a [[Linear_time-invariant_system]] and of LTI system theory; computed for interconnected systems by Mason's rule and used throughout [[Control_theory]] to place poles for stability.   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*   **Microsim — three.js (Wikitube framework), pending deploy:** *Transfer function: one system, three views* will play here once `https://wikitube-3d-microsims.netlify.app/signal/Transfer_function.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Transfer_function.json`; part of the [[Signal_processing]] set ([[PORTAL_Signal_Processing]]).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Transfer_function) : [Wikitube](https://en.wikitube.io/wiki/Transfer_function) ## Previous hub tags Tree parent: [[Control_theory]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*