# Frequency response
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## Microsims — p5.js
### Frequency response (p5.js) · `H(e^{jω})`
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<iframe src="https://editor.p5js.org/sciencenibber/full/FvpfAhYP3" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Frequency response — p5.js microsim"></iframe>
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*How a system's gain and phase vary with frequency — its complete signature for linear signals.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/FvpfAhYP3) · movement *III · Filters & filter design* · 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)*
- [[Cruise_control]] *(in tree)*
- [[Decibel]] *(in tree)*
- [[Digital_signal_processing]] *(in tree)*
- [[Distortion]] *(in tree)*
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## Links (Wikipedia order)
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`Adaptive_control` · `Amplitude` · `Audio_equipment` · `Audio_power_amplifier` · `Audio_system_measurements` · `Automation_and_Remote_Control` · `Bandwidth_(signal_processing)` · [[Block_diagram]] · `Bode_plot` · `Category_6_cable` · `Closed-loop_controller` · `Closed-loop_transfer_function` · `Coaxial_cable` · `Coefficient_diagram_method` · `Control_reconfiguration` · [[Control_system]] · [[Control_theory]] · `Controllability` · [[Convolution]] · [[Cruise_control]] · [[Decibel]] · `Digital_control` · `Digital_filter` · [[Digital_signal_processing]] · `Dirac_delta_function` · [[Distortion]] · `Distributed_control_system` · `Distributed_parameter_system` · [[Electric_motor]] · [[Electrical_grid]] · `Electroencephalography` · [[Electronics]] · `Embedded_system` · `Energy-shaping_control` · [[Fast_Fourier_transform]] · `Fourier_transform` · `Fractional-order_control` · [[Frequency_domain]] · [[Fuzzy_control_system]] · `Fuzzy_logic` · `H-infinity_loop-shaping` · `Hankel_singular_value` · `Hertz` · `High_fidelity` · `Hybrid_computer` · [[Impulse_response]] · `Industrial_control_system` · `Intelligent_control` · [[Kalman_filter]] · `Krener's_theorem` · [[Laplace_transform]] · `Lead–lag_compensator` · `Least_squares` · `Linear_system` · [[Lyapunov_stability]] · [[Mechatronics]] · `Microphone` · `Minor_loop_feedback` · [[Model_predictive_control]] · `Motion_control` · `Multistage_amplifier` · [[Negative_feedback]] · `Nichols_plot` · `Nonlinear_control` · `Nyquist_rate` · [[Observability]] · [[Optimal_control]] · [[PID_controller]] · [[Perceptual_control_theory]] · `Performance` · `Phase_(waves)` · [[Positive_feedback]] · `Programmable_logic_controller` · [[Quantization_(signal_processing)]] · `Radar_jamming_and_deception` · `Radian` · [[Real-time_computing]] · [[Robotics]] · `Robust_control` · `Roll-off` · `Root_locus_analysis` · `SCADA` · [[Sampling_(signal_processing)]] · `Servomechanism` · [[Signal-flow_graph]] · [[Signal_processing]] · `Spectral_leakage` · `Spectral_sensitivity` · `Stability_theory` · `State-space_representation` · `State_observer` · `Steady_state` · `Steady_state_(electronics)` · `Stochastic_control` · [[System_dynamics]] · [[System_identification]] · `Telephony` · [[Time_domain]] · [[Transfer_function]] · `Transient_response` · `Universal_dielectric_response` · `University_of_Michigan` · [[Wayback_Machine]] · `White_noise` · `Window_function` · `Wireless` · [[Z-transform]]
> Signal Processing concept · part of the Signal Processing Portal · movement III · !24 回路 kairo.svg
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*Rendered from the live microsim (▶ motion).*
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## See it next
[](Impulse_response)
*→ [[Impulse_response|Impulse response]]*
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Back to Signal Processing Portal · the room · Semiotic gateway
## What it is
The frequency response is the description of how a system changes the amplitude and phase of each frequency component of an input, expressed as a complex-valued function of frequency.
## How it works / why it matters
It is the Fourier transform of the system's impulse response, and for filters it is usually plotted as a magnitude response (often in decibels) and a phase response. The frequency response reveals passbands, stopbands, cutoff frequencies, ripple, and roll-off, making it the primary tool for specifying and evaluating filters. For a linear time-invariant system, knowing the frequency response fully determines the output spectrum from the input spectrum.
## Signs & universals
Instantiates: frequency amplitude spectrum
## Related
[[Impulse_response]] · Cut-off frequency · [[Filter_design]] · Filter (signal processing) · Fourier transform · [[Linear_time-invariant_system]]
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Frequency_response) : [Wikitube](https://en.wikitube.io/wiki/Frequency_response)
## Previous hub tags
Tree parent: [[Control_theory]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*