Talk:Active noise control

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Reference 2 needs a citation itself

It is used as a citation without any real citation. — Preceding unsigned comment added by 78.162.232.188 (talk) 14:29, 25 January 2020 (UTC)[reply]

Phase vs. polarity

Inverting polarity and shifting phase by 180° are not the same thing. Shifting the phase takes one cycle's worth of time. Inverting polarity is instantaneous.

--Paclopes (talk) 01:21, 4 May 2009 (UTC) Polarity usually refers to the polarity of ligth haves, that are described by a time varying vector field. Sound haves have no polarity. They can be described simply by the variations from the atmopheric pressure level at a given point. I am goingo to remove the references to polarity from the text.[reply]

Ideally, the noise cancellation device flips the polarity of the wave to cancel the noise. This would be the case in noise-cancelling headphones, for instance, where the electric wave can easily start from the microphone, be flipped, and travel to the speaker just in time for the acoustic wavefront to get there.

I left the phase comment in place because I imagine there are other systems where you might actually want a phase shift, if there is some kind of unavoidable delay in the system or something? But maybe it should be changed to polarity, too. - Omegatron 16:41, Apr 15, 2005 (UTC)

That depends on how you implement the phase shifting. If you're doing things digitally, you're breaking down signals into time-independent channels when you do the Fourier transform, so phase and polarity changes are identical. A more accurate description would be to simply say that the system computes a sound to generate that causes destructive interference (cancellation) at the desired location. To call this "reversing polarity" or imposing a "180 degree phase shift" is to grossly oversimplify, as you have to take into account the positions of your cancelling speakers, microphones, and desired silence zones (sound propagation causes a different phase shift in each spectral component, due to finite speed of sound). --Christopher Thomas 23:22, 28 August 2006 (UTC)[reply]

You wouldn't do a Fourier transform if you were just going to flip the polarity. :-) I agree that it should just state what is going on in general at first, as I'm sure different systems have different implementations. Some just flip the polarity, some incorporate a time delay, some incorporate filtering, variable phase shift across the frequency bands, etc. — Omegatron 23:39, 28 August 2006 (UTC)[reply]

I have trouble seeing how any system that didn't work in the frequency domain would work in practice. Something that simply generated a signal with negative amplitude would have have the microphone and the speaker in the same place, which would also have to be right on top of either the noise source or the person who you wanted to insulate from the noise. Even if you're willing to do this, something like a noise-cancelling headphone set would have to use a band-pass filter to allow desired sounds to pass, and for both at-source and at-listener versions you'd have to perform strange tricks to avoid feedback problems (trying to cancel the cancellation signal).

Lastly, a stronger argument occurs to me (which has apparently been stated by others in subsequent threads): Flipping the polarity of the waveform does, in fact, produce a 180 degree phase shift (at least if you're using a sampling window small enough that sound isn't changing much over the window). You've apparently argued below that the mechanism is different, but that assumes a very narrow definition of phase shift (i.e., the operation performed by a causal phase-shifting filter, rather than the phase shift itself). In both engineering and mathematics, the term typically refers to the result only, without requiring the operation to be causal (which is what gives you a delay when implementing a phase-shift filter). --Christopher Thomas 00:36, 29 August 2006 (UTC)[reply]

I have trouble seeing how any system that didn't work in the frequency domain would work in practice.

Not as well. :-) But it would still work. As long as the noise level is lower with the device on than off, it's working. Obviously some implementations work better than others.

In both engineering and mathematics, the term typically refers to the result only, without requiring the operation to be causal (which is what gives you a delay when implementing a phase-shift filter).

Exactly. An active noise control is inherently causal. — Omegatron 02:29, 29 August 2006 (UTC)[reply]

If you are agreeing with my last paragraph, then why are you arguing that "phase shift of 180 degrees" is not correct? If you are disagreeing, please state what parts you disagree with. As-is, your statement appears both confusing and incorrect to engineers and mathematicians for the reasons stated above.--Christopher Thomas 02:54, 29 August 2006 (UTC)[reply]

I don't understand what you're asking. — Omegatron 03:07, 29 August 2006 (UTC)[reply]

Capsule summary of this thread as I've been interpreting it:

O: Inverting polarity and shifting phase by 180° are not the same thing.

C: Yes they are, for reasons X, Y, and Z, and saying they're not confuses scientists and engineers.

O: I agree with your statements, but you're still wrong.

C: Come again?

My apologies if I'm missing something you've said, or haven't expressed my own statements clearly enough, but that's pretty much how I'm presently parsing this conversation. --Christopher Thomas 03:22, 29 August 2006 (UTC)[reply]

Let me try and summarize/summarise:

At the exact point in space where noise cancellation is actually taking place, the antinoise waveform is polarity flipped from the noise waveform, thus causing destructive interference.

At that same point in space, the antinoise waveform (taken as a whole) is not phase-shifted 180 degrees from the noise waveform; this would not cause destructive interference.

But if you could take the Fourier transforms of both the noise and antinoise waveforms, you'd find that each individual sine wave component within the antinoise waveform is both polarity-flipped and 180 degrees opposite in phase from its corresponding sine wave component in the noise waveform. This is because, for the specific case of a sine wave, there's no distinguishment between being "polarity flipped" and 180 degrees phase shifted.

Everyone: have I sumari[zs]ed this correctly?

Atlant 13:04, 29 August 2006 (UTC)[reply]

Pretty much. To rephrase my complaints:

The term "phase shifting a signal" is ambiguous, as it could mean "delaying a repeating (or short-time stationary) signal by a fraction of its fundamental frequency" or "delaying each frequency component individually by an equal fraction of a cycle", which have completely different effects:
- Delaying an entire wave by a fraction of its cycle can be used for noise cancellation (as described in the first section of the first patent of such a system)
- Phase shifting each frequency component by any value other than 180° would not be as useful (unless the medium is dispersive?)
I think that using the term "phase shifting" is highly misleading, when the actual electronics merely flip the wave. I'm aware that the output waveforms are mathematically equivalent in a non-causal theoretical treatment, but the actual device is just flipping the signal over, and it's misleading to imply otherwise. It's not doing an analog-to-digital conversion, applying an FFT, shifting the phase of each component, inverse transforming, and doing a digital-to-analog conversion. It's not applying an all-pass filter with a constant phase shift for each frequency, set to 180°. (Both of which would require a time delay.) It's just flipping the black and the red wires. — Omegatron 13:55, 29 August 2006 (UTC)[reply]

This appears to summarize things, but I feel strongly that saying that "inverting polarity and shifting phase by 180° are not the same thing" is at least as misleading, because for us signal-processing types, phase shifting is usually interpreted as referring to each of the component frequencies.

Would a phrasing along the lines of, "...implemented by inverting the polarity of the waveform, which has the effect of altering the phase of each frequency component by 180 degrees, causing destructive interference" be acceptable to you? It would certainly go a long way towards eliminating my concerns (and apparently the concerns of other responders), while hopefully avoiding the ambiguity which you're objecting to. --Christopher Thomas 02:18, 31 August 2006 (UTC)[reply]

because for us signal-processing types, phase shifting is usually interpreted as referring to each of the component frequencies.

That's simply not true. Terms like "phase shift" are ambiguous when talking about anything except sinusoids. Most of the time, they are actually interpreted to refer to the cycles of a repeating waveform as a whole; not the individual frequency components, though both meanings are valid:
Phase shift: A change in phase of a periodic signal with respect to another periodic signal or reference signal.[1]
Phase: A time based relationship between a periodic function and a reference. In electricity, it is expressed in angular degrees to describe the voltage or current relationship of two alternating waveforms.
Phase Difference: The time expressed in degrees between the same reference point on two periodic waveforms.[2]
Phase: A particular angular stage or point of advancement in a cycle; the fractional part of the angular period through which the wave has advanced, measured from the phase reference.
Phase Shift: The angular difference of two periodic functions.[3]
Phase: The timing of a sound wave that is measured in degrees from 0-360.
Phase Shift: Frequency interaction ... which can cause some frequencies to be delayed with respect to other frequencies.[4]
phase shift: The change in phase of a periodic signal with respect to a reference.[5]
phase difference: The time interval or phase angle by which one wave leads or lags another.[6]; Besides, even if it does have a well-defined meaning in a certain field, Wikipedia is not field-specific, so we can't just say it has one particular meaning when it has a variety of meanings in general usage.

Would a phrasing along the lines of, "...implemented by inverting the polarity of the waveform, which has the effect of altering the phase of each frequency component by 180 degrees, causing destructive interference" be acceptable to you?

Not really. To reiterate:

I'm very well aware that $\sin(\omega t)+(-\sin(\omega t))=\sin(\omega t)+\sin(\omega t+\pi )=0$ . Really. They are mathematically equal. I know this.
For a non-sinusoidal signal, a polarity flip is mathematically equivalent to shifting each individual frequency component by 180 degrees. Yes, I know.

But you could also say

\sin(\omega t)+\sin(-\omega t)=0

. No one is calling it "time-reversal cancellation". You could say

\sin(t)+\int {\int {\sin(t)\,dt}\,dt}=0

, but no one is implementing a circuit with double integrators to achieve the same result as an inverter. It is misleading to say you are phase canceling when you are really polarity canceling. Yes, the outputs are indistinguishable, but the method is not.

Also, in real, practical systems, the method used will never achieve ideal mathematical results, anyway, so you will only have partial cancellation, and the methods used will be distinguishable.

\sin(\omega t)+(-0.99\sin(\omega t))\neq \sin(\omega t)+\sin(\omega t+0.99\pi )

Also, different physical devices use different methods with varying degrees of cancellation. The simplest, and most well-known, is to just invert the polarity (which certainly does not require performing a Fourier transform, as you seemed to imply above), but there are more advanced methods with better results. We need to document this in detail. So in the intro, we just say "...implemented by generating a wave that causes destructive interference". Later, we say "The simplest and most well-known method is to invert the polarity, which cancels out waves adequately in certain conditions, such as plane waves in ducts or localized low frequency..." "A more complex method uses adaptive filters to... " and detail each type.

"How can I create a simple sound cancellation device?" and the Active Noise Control FAQ contain information that we should cover here. — Omegatron 16:55, 5 September 2006 (UTC)[reply]

Comments to phase vs. polarity

ANC systems actually use both polarity inversions and phase shifting, depending on the controller strategy. There are two types of control strategies: feedback and feedforward.

- In a feedback control system, the signal you want to cancel (error signal) is fed to the controller. Commonly, a polarity inversion and some filtering are used, which may cause phase shifting. This type of strategy is the simplest one, but can only be used when the delays between the speaker and the error microphone are small; otherwise the system becomes unstable. Also, when using feedback controllers, it's not possible to cancel in the whole frecuency range, in fact there are always amplifications in some frequency bands. It can be done using analog devices.

- In a feedforward control system, a reference signal and the error signal are fed to the controller. The reference signal is correlated with the sound you want to cancel; in other words, it gives the controller information about the signal it has to cancel. The controller then uses a minimization algorithm to compute the appropriate filter so that the filtered reference signal emitted trough the speaker minimizes the error signal. In this case filters are used, which shift the phase of the reference signal. It is possible to obtain cancellation in a frequency range without causing amplifications in other bands. This strategy needs complex calculations, so a DSP or other computer system are required.

In any case, when defining the concept of destructive interference, the signals have opposite phase in a mathematical sense, regardless of how you obtain that difference of phase in practise, by inverting polarity or shifting the phase. --Alejandroff 11:50, 19 October 2005 (UTC)[reply]

This paper defines them differently. It says feed-forward is for canceling a repeating signal that is already well-known, and feed-back is for canceling unpredictable noise from the environment. — Omegatron 14:04, 5 September 2006 (UTC)[reply]

If you are talking about the small description in (Rafaely and Jones 2002), that is just talking about what they did in the experiment, which was about headsets. Talking in general, it is clear that with a feedback controler you can only obtain sound reduction in a certain frequency range. The width of this range will depend mainly on the delay between the error microphone adn the secondary speaker. In a headset, this delay is obiously small, but in almost all other application of ANC, this is not the case.

Feedforward controllers only need a reference signal, in other words, you need a signal correlated to the noise you want to cancel. All you need is that reference signal, you don't need it to be periodic, it can be white noise, for example. The band you can control is basically the band of the reference signal; that is, if the reference signal has power in one frequency band, in principle you can obtain canelation. [7] this article refered here, in which i particiapted, discribes an example of broadband noise cancelation of a white noise signal using a feedforward controller.

Nelson, P. A. and Elliott, S. J., 1992. Active Control of Sound. Academic, London.

Elliott, S. J., 2001. Signal Processing for Active Control. Academic Press.

Kuo, S. M., and Morgan, D. R., 1996. Active noise control systems. John Wiley & Sons, Inc.

Those references are good books that explain all this methods deeply. — Alejandroff 02:22, 5 November 2006 (UTC)[reply]

More on phase versus polarity

I've just removed the several comments in the article that incorrectly stated that the antinoise signal was not a phase-reversed version of the noise. I suspect the problem was that these statements were phrased too simply to be meaningful, but it's easily shown using the Fourier transform that, for those frequency bands where noise cancellation is taking place, the various frequency components of (that is, the multiple sine waves that constitute) the antinoise signal are most definitely phase-reversed from their analagous components in the noise signal; that's why destructive interference takes place. In the time domain, the antinoise is polarity reversed. In the frequency domain, it's phase-reversed (which, for a sine wave, also happens to be polarity-reversed, frequency-by-frequency).

I think this is probably too difficult to explain in the article, but if someone wants to take a crack at being bold and explaining it, please be my guest!

Atlant 12:18, 10 August 2006 (UTC)[reply]

There's a lot of confusion about this: [8] [9] [10] [11] [12] — Omegatron 14:54, 10 August 2006 (UTC)[reply]

(that is, the multiple sine waves that constitute) the antinoise signal are most definitely phase-reversed from their analagous components in the noise signal

But you didn't go in and phase-shift each individual frequency component; you flipped the whole signal over.

Such a phase shift in a real-life system would require a delay. — Omegatron 19:31, 25 August 2006 (UTC)[reply]

No, not for pure sine waves where a polarity reversal and a 180° phase shift are functionally identical: no delay required.

Atlant 18:11, 27 August 2006 (UTC)[reply]

Functionally identical, but not identical. In a real-life system, a phase shift requires a delay. A phase shift of 35° and a phase shift of 180° are more closely related than a polarity flip. — Omegatron 19:24, 27 August 2006 (UTC)[reply]

I'm sorry, but you're wrong. For a sine wave, the results are indistinguishable.

Atlant 02:22, 28 August 2006 (UTC)[reply]

That's what I just said. The results are indistinguishable, but the methods used are not. — Omegatron 03:04, 28 August 2006 (UTC)[reply]

Active Noise Controller

I would like to know about the companies who can supply active noise cancellation ear defenders and also DSP based active noise controller (with adaptive algorithm or LMS- & FXLMS algorithm.

Thanks for your valuable reply.

Google would be the obvious place to start.

By the way, you can "sign" your talk postings by including four tildes (~~~~) after your post. When you press "Save page", these will be converted into your username or IP address in a handy, Wikilinked format. A timestamp for your post will also be included.

Atlant 14:03, 17 February 2006 (UTC)[reply]

A removed description

I've removed this recently-added text from the article. To me, the description farther up in this talk page is more accurate. This newer description doesn't include the simple nearly-instantaneous, band-limited feedback mechanism that is commonly used in ANC headphones.

Several different types of noise cancellation are possible. First is feedback, where a periodic signal is processed to produce a periodic signal of the opposite phase at a certain location of space, usually near an error microphone. This requires the noise signal to be periodic. Secondly is the feedfoward system, in which noise is recorded along a path between the noise and cancellation actuator(s). In a causal system, noise is recorded close to the source such that sound of an opposite phase can intercept it along a path. This system does not require the signal to be periodic.

Atlant 21:35, 20 March 2006 (UTC)[reply]

Unfortunately this description is much better than the one in the article. It has the virtue of being more complete. The article concentrates overmuch on FFT based, periodic, type cancellation. Real world cancellation of impact type noise has been demonstrated, and the sstem I used was based on time history filtering, not FFTs. Greglocock 10:18, 22 February 2007 (UTC)[reply]

Applications

Shouldn't this page talk about, well, applications? Like military firing ranges, high-noise industrial areas? The first part actually seems to be talking about Types. Bihal 05:45, 28 April 2006 (UTC)[reply]

Yes. Please be bold and add to the article!

Atlant 13:13, 28 April 2006 (UTC)[reply]

Phase Cancellation of Visible Light Rays [?]

I'm curious as to whether it is (at least theoreticaly) possible to cancel the light rays of the visible spectrum through polarity reversal and/or 180° phase shift.

Could it be possible to generate a frequency that effectively cancels the phases of the ROYGBIV light rays?

And if so, then... 1.) would this create a state of total darkness?, or rather some other visible sensation? And... 2.) could such a high frequency possibly be generated with extant radio and multimedia hardware?

[It's a big question, but also one that has been nagging at me for quite some time :P ] Pine 16:20, 18 July 2007 (UTC)[reply]

Check out wave particle duality, and coherence, and interferometry. Roughly speaking, yes it is sort of possible, but only for 'short' distances. Greglocock 03:45, 21 July 2007 (UTC)[reply]

with the current technology it would be possible to accuratly control the phase of a very short laser puls (femtoseconds long) at a chosen frequency using high-resolution spectral phase shapers. Using two of these setups in a controlled environement would cause cancelation of the lightpuls. But to cancel a short controlled puls is something entirely different than to cancel a diffuse lightsource with a wide spectrum. Creating the right frequencies could be done using liquid cristals (LCD screens), but since the area in which a random lightsource would be coherent with the generated cancelation source is only several nanometers at max, the cancelation area would also be several nanometers, shorter than the wavelenght of light (800nm) and therefor does only alter the light, not cancel it. (i'm no optical scientist; imperfection at complete certainty) Frodo Muijzer (talk) 10:37, 23 October 2008 (UTC)[reply]

Polarity v. phase again

I can't see any support for the idea that sound waves have "polarity" at all—rather (mainly)) electrical signals do (as do light waves). It appears that one (but not the only) way to generate a phase-reversed wave is to invert the polarity of a signal simultaneously. Are there any references to the polarity of sound waves in the first place? ^Bongo_matic 05:36, 3 December 2009 (UTC) hello i live nest to people that will not shut up .. i wanted to makes my computer shut them up. can i do this some how.. come on people it's 2011 —Preceding unsigned comment added by 74.215.3.182 (talk) 21:04, 6 March 2011 (UTC)[reply]

I agree that sound waves do not have the kind of polarization (waves) that light waves have.

I hope you agree with me that rapid changes in air pressure -- above and below some average air pressure -- are perceived as sounds. Also, I hope you agree with me that if the air pressure at the ear is maintained at some extremely slowly changing or constant pressure, no sound can be heard.

When a speaker pushes out on the air in front of it, that causes the air to compress to a slightly higher-than-average air pressure. When a speaker pulls in, that causes rarefaction in the air to a slightly lower-than-average air pressure.

In this article, by "invert the polarity", we mean that (a) when some noise source causes rarefaction, the anti-noise speaker pushes out, also (b) when some noise source causes compression, the anti-noise speaker pulls in. In both cases, maintaining the air -- at the ear -- at very close to the average air pressure, so very little sound can be heard.

Is there some way other than "invert the polarity" that would be just as easy to understand and avoid the incorrect implication that sound waves have polarization (waves)?

How can we improve this article to make it easier to understand? --DavidCary (talk) 13:47, 16 March 2013 (UTC)[reply]

Theory and References

I plan on adding more theory on the physics behind Active Noise Control. Additionally I think providing more information from reliable white paper research will enhance the article. Bartscrc-NJITWILL (talk) 01:45, 10 November 2011 (UTC)[reply]

Trumpets

Dumb post - Has this been used/tried for trumpets. Even the best trumpet practice mutes don't sound that good/real ( at least to me ) and the back pressure is distressing ( at least to me ). If a device could be attached... to a trumpet bell could it kill the sound in the room while I blasted away and got a more real but reduced sound in a headphone. 24.128.186.53 (talk) 00:19, 12 February 2015 (UTC)[reply]

I'd say it is possible to reduce the average sound level, but I doubt you'd easily quieten the initial attack phase. Not a dumb question at all actually. Greglocock (talk) 02:22, 12 February 2015 (UTC)[reply]

Another dumb question ( seeing as how this site seems to have engineers/phd;s/? on it ) - is it the difference notes, the rapid chance in notes and/or the range of notes that make this hard to do. If it was easy I suspect some manufacturer - Yamaha/Bach/etc would have done tis long ago. Why does the "initial attack phase matter"? Another dumb question - why is the "initial attack phase" different and/or a problem. Thanks 2601:181:8301:4510:A1F7:777A:2085:58A (talk) 15:03, 30 April 2018 (UTC)[reply]

Initial attack phase? Someone ought to tell Chris Goldscheider. But I guess it's a bit late now. Martinevans123 (talk) 15:59, 30 April 2018 (UTC)[reply]

Eurovision anti-booing technology

I have seen no evidence at all that this uses ANC, which would be tricky in any case. The only technical description suggests they are using masking, ie drowning out the boos with applause. Greglocock (talk) 03:21, 12 July 2015 (UTC)[reply]

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Are there any working sound cancelling machines that I can buy?

Non ear phones, for places like apartments etc? What is the reason there are mostly only Sound Canceling Ear Phones? — Preceding unsigned comment added by 0wl (talk • contribs) 18:20, 10 February 2017 (UTC)[reply]

@0wl: Active noise cancellation can only be applied to headphones because the noise profile that needs to be cancelled differs significantly from location to location (even across the small space of an apartment). A noise signal that might cancel out ambient noise at your couch might significantly add to that same noise in your kitchen, etc. WikiDan61^ChatMe!_ReadMe!! 18:49, 10 February 2017 (UTC)[reply]

Fantastic reply, Dan, thank you! — Preceding unsigned comment added by 0wl (talk • contribs) 19:01, 10 February 2017 (UTC)[reply]

I'm glad you think its fantastic but it is wrong. Noise cancellation in large volumes is practical, and does not necessarily increase the noise anywhere outside of the cancellation area. For instance, many years ago somebody built an exhaust noise canceller for a ship. That seems to have worked quite well. I installed a noise cancellation system on a car's outside to reduce the exhaust noise. It was successful but impractical. In resonant cavities such as inside a car the cancellation system does not work the way you think it might, effectively it couples the acoustic resonances to the electronics, and the sound energy is turned into heat. However there is no effective general purpose ANC system that I know of. I could probably knock one together for a specific environment, but it would not be cheap. Also there are some noises that would be very hard to cancel. The reason it works well with engines and things like that is that you know exactly what the frequency is that you need to kill. It is possible to cancel non deterministic noise in some cases, but not in general. Greglocock (talk) 23:46, 10 February 2017 (UTC)[reply]

... "exhaust noise canceller for a ship."^{[citation needed]} Martinevans123 (talk) 23:50, 10 February 2017 (UTC)[reply]

Sorry, I haven't worked in that field for 27 years, I can't remember who did it (Lord I suspect) or the timeframe, 60s probably. Here's a neat summary of ANC, including a discussion of free field cancellation and a refutation of the statement about noisier elsewhere - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.569.5748&rep=rep1&type=pdf and here's a more modern ship based system http://www.jime.jp/e/publication/bulletin/english/pdf/mv29n012001p35.pdf . Incidentally the first ANC demo by Lotus used a very simple setup that was manually tuned on the fly, basically fiddling with the phase and amplitude of the speaker by fiddling with two knobs. Greglocock (talk)

Actually, both statements are somewhat correct. There are basically two different approaches to cancelling noise: 1) cancelling noise locally at a specific point via a control source that is placed away from the noise source or 2) cancelling noise globally with control sources which are very close to the noise source. The second approach uses the fact that the total sound power output can be minimized, if the noise source and the control source are closer than half a wavelength apart. That means for the first approach, that the total sound power is always increased if the distance is larger than half a wavelength (see e.g. section 8.4. in Nelson and Elliott, "Active Control of Sound", Academic Press, 1992). Fhchl (talk) 15:16, 16 September 2021 (UTC)[reply]

Hyundai RANC

I realise without refs this cannot go into the main article, but the first time I saw an accelerometer based feedforward ANC to cancel road noise was in the late 80s at Lotus. It was fitted to a large Audi and a Porsche. I don't know if either company took it to production. Hence Hyundai's claim of a 'first' is rather inaccurate. Greglocock (talk) 07:29, 20 February 2020 (UTC)[reply]

Adaptive noise cancellation

Need your thoughts on whether this should be a separate topic from Noise cancellation or Adaptive filtering. It appears to be someone's research material. Please help discuss at Draft:Adaptive noise cancelling#Notability for this. AngusW🐶🐶F (bark • sniff) 18:52, 21 January 2023 (UTC)[reply]