Active_noise_control - Wikiparency

# Active noise control **Active noise control** (ANC), also called active noise cancellation or active noise reduction, is a technique for making an unwanted [[Sound|sound]] quieter by producing a second, carefully shaped sound that combines with it and largely cancels it, rather than by blocking, absorbing or damping the original sound mechanically. A reference sensor picks up the unwanted sound, a controller computes a matching wave that is close to its exact inverse, and a loudspeaker emits that anti-noise so that where the two pressure waves meet they add to something much smaller than either alone; an error microphone measures how well the cancellation is working and feeds that measurement back so the system can correct itself. Because the controller must keep re-aiming this cancellation as conditions change, from a shifting engine speed to the exact position of an ear against a headphone cushion, practical systems build it around an adaptive filter rather than a fixed one, making active noise control one of the standard applications of [[Audio_signal_processing|audio signal processing]] outside of communications and recording. The primary microsim on this page reduces the problem to the single case that shows why it is unforgiving: one steady tone and its would-be cancelling twin. Dragging the anti-noise wave's phase away from perfect inversion shows how quickly a system that is cancelling well can tip over into making the noise louder than if it had done nothing at all. ## Explanation Active cancellation works by superposition. If the unwanted sound at a point in space is a pressure wave `d(t)` and a speaker adds a second wave `y(t)` at the same point, the pressure actually present is their sum, `e(t) = d(t) + y(t)`; setting `y(t)` to the exact negative of `d(t)` drives `e(t)` to zero. For a single steady tone, writing the primary noise as `d = cos(psi)` and the anti-noise as `y = r*cos(psi + theta)` with amplitude ratio r and phase θ relative to the primary, the residual that reaches the ear is itself a sinusoid of amplitude `R = sqrt(1 + r^2 + 2r*cos(theta))`, which reaches zero only at the ideal point, equal amplitude and exact inversion. Writing the phase error away from that ideal inversion as φ, the residual with equal amplitudes collapses to `R = 2*|sin(phi/2)|`: a small phase error is forgiving, since R grows only gradually at first, but at φ = 60° the residual equals the primary noise on its own, meaning the anti-noise has bought nothing, and beyond 60° the combination is louder than doing nothing. Because phase is measured against one period of the tone, a fixed timing error, from the sound's travel time between sensor, processor and speaker, from an imperfect model of the acoustic path, or from nonlinear [[Distortion|distortion]] introduced by the loudspeaker itself, is a much larger phase error at a high frequency than at a low one. In the sketch, which slows its tone down to between 1 and 20 Hz so the waveforms are visible on screen, reaching a useful −10 [[Decibel|dB]] of attenuation needs the phase error held under about 18°, and −20 dB needs it under about 6°; at the sketch's default 4 Hz those thresholds correspond to timing budgets of about 12.5 and 4.2 milliseconds, shrinking further as the tone frequency rises. The same scaling holds at real acoustic frequencies: a millisecond of uncompensated delay is a small fraction of a period at 50 Hz but is most of a full cycle by 1 kHz, which is the physical reason active systems reliably knock down low-frequency drone and struggle with high-frequency hiss. Holding the phase and amplitude exactly right is hard precisely because the acoustic path keeps changing: a listener's ear moves relative to a headphone driver, an engine's dominant tone drifts with load and speed, a road surface changes under a tyre. Practical systems therefore replace the fixed anti-noise above with an adaptive filter that recomputes its own coefficients many times a second from the error microphone's ongoing measurement, continuously re-aiming the cancellation at whatever the primary noise is doing now rather than at what it was doing when the system was designed or last tuned. ## History The earliest known proposal for cancelling sound with sound came from the German physicist Paul Lueg, who filed a patent in 1934, granted in 1936, describing a system that picked up an unwanted sound electrically, inverted it, and re-radiated it to interfere destructively with the original; the patent already identified the two hardest parts of the problem, generating a true inversion and delivering it so that it meets the original wave at the right place and time.[^anc-lueg] Turning the patent into a working system awaited both practical transducers and, decades later, electronics cheap enough to compute the required anti-noise continuously and adaptively rather than for one fixed tone; research through the 1950s and 1960s, much of it aimed at aircraft and industrial noise, gradually closed that gap.[^anc-fogel] The adaptive filter that does this recomputing in a modern system is usually trained by some variant of the least-mean-squares algorithm that Bernard Widrow and Marcian Hoff introduced at Stanford in 1960 for an unrelated adaptive-circuit problem and that was later adapted specifically to cancel a reference signal from a desired one.[^anc-lms] Commercial active noise-reducing headsets for aviation use reached the market in the late 1980s, led by Bose Corporation, and the same principle was extended over the following decades to consumer headphones, earbuds, road vehicles and mobile handsets as [[Digital_signal_processing|digital signal processing]] became cheap enough to embed in a headset or a dashboard itself, an era of research tracked largely through [[Institute_of_Electrical_and_Electronics_Engineers|IEEE]] signal-processing journals and conferences.[^anc-bose] ## Applications Aviation remains the application where active noise control is most valuable and most mature: a propeller or turbine cabin is loud, dominated by tones below a few hundred hertz that are exactly the regime active systems handle well, and pilots already wear headsets that place a speaker, and for the pilot's own microphone, close to the ear, simplifying the acoustic path a system needs to control. Consumer headphones and earbuds are now the largest application by sheer volume, using one or more microphones on the earpiece to sense the noise entering around or through the cushion and driving a matched anti-noise signal from the very driver that plays music, so the same acoustic path serves both jobs; commercial models typically claim on the order of 15 to 20 [[Decibel|dB]] of additional low-frequency attenuation on top of whatever passive isolation the earcup already provides.[^anc-attenuation] Road vehicles apply the same idea to the boomy, largely tonal low-frequency noise transmitted through the chassis from the engine and road, driving cancelling tones through the existing audio system's speakers and sensing the result with microphones mounted in the cabin roof or seats. Industrial and building installations cancel the drone of ducted fans and compressors inside ductwork, an environment close to the easiest case active control has: one confined acoustic path, one dominant tone, one loudspeaker. ## Active versus passive noise control Passive noise control is the older and more familiar half of building [[Acoustics|acoustics]]: it blocks or absorbs sound with mass, stiffness or porous material, a heavy panel reflecting sound because it is hard for the wave to set such a heavy surface in motion, and a porous absorber converting a sound wave's motion into heat through friction in its pores. Passive treatments work best at mid and high frequencies, where the wavelength is short enough to be small compared with a practical thickness of material or panel; treating 100 Hz sound this way, at a wavelength of roughly 3.4 metres in air, generally means either an impractically thick absorber or a very heavy, well-sealed barrier. Active noise control is the mirror image: it needs almost no bulk, since a loudspeaker and a little electronics can in principle cancel a tone of any wavelength, and it works best exactly where passive treatment struggles, at low frequency, for the phase-budget reason given above. It is also inherently local, cancelling well only in a small region near the error microphone rather than filling a whole room the way a thick absorber does, and it is limited by more than the phase-and-timing budget: the sensing and amplification chain has its own [[Noise_(electronics)|electronic noise]] floor, part of it thermal ([[Johnson–Nyquist_noise|Johnson-Nyquist]]) noise in the microphone and amplifier and, in a digital implementation, [[Quantization_(signal_processing)|quantization]] noise from the analogue-to-digital step that turns the error microphone's signal into numbers the adaptive filter can use, and no amount of clever filtering cancels a noise floor that is not correlated with the reference signal at all, which ultimately caps the [[Signal-to-noise_ratio|signal-to-noise ratio]] any active system can reach.[^anc-quant] In practice the two approaches are complementary: an aviation or automotive system leans on passive damping and sealing for the mid and high frequencies, where it is cheap and effective, often adding a [[Low-pass_filter|low-pass filter]] ahead of the adaptive canceller so its effort is spent only where active cancellation can help, and reserves active cancellation itself for the stubborn low-frequency tones passive treatment cannot reach without unacceptable weight or bulk. ## Microsims The primary microsim carries four linked views of one steady tone and its cancelling twin. A time scope scrolls three lanes, the primary noise, the anti-noise and their sum, so cancellation is visible directly as the third lane flattening toward a straight line; a phasor diagram draws the same two waves as rotating vectors placed tip to tail, so the residual is literally the vector that closes the triangle, the geometric reason a phase error, and not only an amplitude error, matters; an attenuation curve plots the decibel result over the full range of phase error with a marked 0 dB line above which the anti-noise is doing more harm than good; and a diagnostics panel prints the residual, its decibel figure, and the timing slip the current phase error represents at the chosen tone frequency. `phase error`, `amplitude ratio B/A` and `tone frequency` are the three labelled sliders, each with a live readout. A three.js companion sketch, not carried on this page, renders the same anti-noise path in more depth, showing the residual fall as an adaptive filter's weights converge rather than being set by hand. *Try:* Drag the phase-error slider away from 0° while watching the attenuation readout, and find the phase magnitude at which the number crosses 0 dB and the anti-noise starts making the tone louder instead of quieter. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Active_noise_control) : [Wikitube](https://en.wikitube.io/wiki/Active_noise_control) Skeleton mirrored at revision 1371808139. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Audio_signal_processing]] - [[Digital_signal_processing]] - [[Low-pass_filter]] - [[Signal-to-noise_ratio]] - [[Decibel]] - [[Noise_(electronics)]] - [[Quantization_(signal_processing)]] - [[Acoustics]] ## Notes The sketch's tone frequency, adjustable from 1 to 20 Hz, is chosen so the waveforms scroll slowly enough to watch, not because active noise control operates at those frequencies; it stands in for the same phase-versus-period relationship at real acoustic frequencies of tens of hertz to several kilohertz. It also treats the primary noise as a single pure tone with a fixed amplitude ratio and phase error chosen by the reader, rather than the broadband, time-varying noise and continuously self-adjusting filter of a real system. ## References The superposition and phasor algebra used in Explanation (destructive interference, `R = 2|sin(phi/2)|`) is direct trigonometry and is not separately footnoted, per Wikitube style guide §6.1. [^anc-lueg]: Lueg, P. "Process of Silencing Sound Oscillations." U.S. Patent 2,043,416, filed January 1934, issued June 9, 1936. Google Patents: https://patents.google.com/patent/US2043416A . [^anc-fogel]: Citation needed: a primary paper or patent record for the specific 1950s-1960s aviation and industrial active-noise-control development work referenced here (researchers, organisations, dates) would let this sentence name them. [^anc-lms]: Widrow, B.; Hoff, M. E. Jr. "Adaptive Switching Circuits." *IRE WESCON Convention Record*, part 4, 1960, pp. 96-104. [^anc-bose]: Citation needed: a company or trade-press record for the exact year and model of Bose Corporation's first commercial active noise-reducing aviation headset would let this sentence give a precise date rather than "the late 1980s." [^anc-attenuation]: Citation needed: a manufacturer's or independent test lab's measurement report for typical consumer ANC headphone attenuation figures would let this sentence cite a real measurement rather than an approximate range. [^anc-quant]: Dyer, J.; Davis, C. *Measurement and Instrumentation: An Introduction to Concepts and Methods*, 1st ed. 2020, pp. 39-40 (PDF pages), for the quantization relation `SNR = 6.02N + 1.76 dB`. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods . CC BY-NC-SA. ## External links - [Noise cancelling — live microsim](https://editor.p5js.org/sciencenibber/full/ARZDueI-Y) - [Noise cancelling — sketch source, p5.js editor](https://editor.p5js.org/sciencenibber/sketches/ARZDueI-Y)