How do noise cancelling headphones *really* work?

[ebastler]

Just curious... I have Googled and read a bit, but find the explanations I came across unsatisfying. Sure, in principle you want to measure the incoming environmental noise with a microphone mounted to each ear's headphone; then add an inverted copy of the signal to the signal driving the respective speaker. But how does this actually work in practice?

(a) I assume that there is a phase delay in the microphone, and in driving the speaker. So if you simply invert the microphone's signal, your resulting speaker output will probably be "too late" -- right?

(b) So, do real-world noise cancelling headphones actually delay the microphone signal further, by a bit less than 180°, so that the previous wave cycle received on the microphone drives the speaker, to interfere with the next incoming wave? The fact that noise cancelling headphones apparently can't handle one-off impulse signals is consistent with that assumption.

(c) But, of course, a "bit less than 180° delay" means a different delay time for each frequency component. Does the signal processing actually include an FFT, frequency-dependent time delay, and re-synthesis? Or some clever all-pass filter with the right frequency-dependent delay characteristics?

(d) Finally, how do you determine the amplitude of the cancelling signal you need to feed to the phones? Even without the active cancellation, only a dampened version of the incoming sound will reach the ear, due to the headphone's passive noise dampening. One needs to supply an inverted signal with the same (frequency-dependent) amplitude. Do the manufacturers just characterize the frequency-dependent passive dampening once, in the lab, and assume that it will be the same for each person wearing the headphone? Or is something more clever going on?

I'd appreciate any insights you might have on this -- and any references to technical literature. Thanks!

EDIT: Fixed mangled sentence in point (a) above...
And adding one more question:

(e) Several publications and DSP app-notes deal with "active feedback" noise cancellation schemes, which assume the presence of another microphone (behind the speaker), to detect and minimize an error signal. But do commercial ANC headphones have such error detection microphones?

[Mr. Scram]

Interesting question. I won't pretend I have a clue, but I'd love to see the input of others.

[GeorgeOfTheJungle]

I don't know, I'm only guessing but... if you sample the inputs and delay the output just a bit (some ms) it seems easy to substract the "ambient noise" sampled signal from the "voice input" sampled signal and deliver that some ms later to the output.

[tautech]

IME you betcha they work, well the good stuff does.

In those I have used they were both Bose, a professional Aviation headset and their QuietComfort 35.

[ebastler]

IME you betcha they work, well the good stuff does.

I don't doubt that they work -- but how do they do it? 

[ebastler]

I don't know, I'm only guessing but... if you sample the inputs and delay the output just a bit (some ms) it seems easy to substract the "ambient noise" sampled signal from the "voice input" sampled signal and deliver that some ms later to the output.

No, that won't work. Some of the environmental noise reaches your ears directly, via the headphone's less-than-perfect passive dampening. And you have to cancel that out immediately, via a speaker output signal that interferes destructively with the "real" soundwaves reaching your eardrum. No delay allowed!

[GeorgeOfTheJungle]

Ahh, ok, I see. I was not thinking a pilot in a cockpit but the mobile phones' noise cancellation. Perhaps that's a different beast?

[ebastler]

Ahh, ok, I see. I was not thinking a pilot in a cockpit but the mobile phones' noise cancellation. Perhaps that's a different beast?

Right -- subtracting background noise (captured via a second microphone) from the speech signal you want to send down the line to a remote party is probably an easier task. The source signals are better defined and "symmetrical", since they are both captured via microphones, and you can allow for a few milliseconds of delay for digital signal processing.

But I was thinking of the noise-reducing headphones, as used by pilots. (Or airline passengers, office workers wanting a quiet environment, etc. -- Bose's "QuietComfort" headphones are the best-known example of consumer versions.)

[wraper]

(a) I assume that there is a phase delay in the microphone, and in driving the speaker. So if you simply invert the microphone's signal, your resulting speaker output will probably be "too late" -- right?

Why do you think there is significant delay between microphones and speakers? On top of that, electrical signal from microphone to speaker travels almost instantly (if we assume there is no digital processing delay) while actual ambient sound still has to travel the distance to your ear.

[wraper]

Where phase shift will matter the most is high frequencies but, first of all, damping them is much easier and ear is much less sensitive to them as well.

[wraper]

https://www.infineon.com/dgdl/Infineon-AN538_Infineon_microphone_in_Noise_cancelling_headsets-AN-v01_00-EN.pdf?fileId=5546d462602a9dc801607a0e96951aa6

[ebastler]

To answer the last of my own questions (point (e) above), the Bose headphones do indeed have another microphone which captures the speaker output. See this teardown video, from 9:45 onwards:



That does open up a lot of possibilities, of course -- e.g. optimizing the amplitude (as a function of frequency) of your correction signal, depending on how well the passive dampening fits the current user's ears etc.

I wonder whether even the small in-ear phones (e.g. Bose QC 20) have room for those error detection mics? @Dave, how about a teardown video?

[ebastler]

(a) I assume that there is a phase delay in the microphone, and in driving the speaker. So if you simply invert the microphone's signal, your resulting speaker output will probably be "too late" -- right?

Why do you think there is significant delay between microphones and speakers? On top of that, electrical signal from microphone to speaker travels almost instantly (if we assume there is no digital processing delay) while actual ambient sound still has to travel the distance to your ear.

Right, the microphone probably contributes the smallest delay; but I would assume that driving an inductive speaker does incur non-negligible phase shifts? And even more so the A/D and D/A conversion required for digital signal processing.

I agree with your other post that this becomes more relevant at higher frequencies. And indeed at frequencies above a few kHz the typical consumer ANC headphones seem to rely on passive dampening only. But still, even at the frequencies below that limit, they seem to do more than just "invert and add" -- as witnessed by the presence of an error detection microphone.

Thanks for the Infineon appnote! Hadn't found that one.

[tautech]

To answer the last of my own questions (point (e) above), the Bose headphones do indeed have another microphone which captures the speaker output. See this teardown video, from 9:45 onwards:



That does open up a lot of possibilities, of course -- e.g. optimizing the amplitude (as a function of frequency) of your correction signal, depending on how well the passive dampening fits the current user's ears etc.

I wonder whether even the small in-ear phones (e.g. Bose QC 20) have room for those error detection mics? @Dave, how about a teardown video?

Well those aren't exactly the TOL set, are they ?

From the QC35 blurb:

But we didn’t stop there. We made them even better, because the Action button lets you adjust your level of noise cancellation between three different levels. And you can set it to the one that feels right for your environment and your music.

https://www.bose.co.nz/en_nz/products/headphones/over_ear_headphones/quietcomfort-35-wireless-ii.html#v=qc35_ii_black

[ebastler]

Well those [Bose QC 25] exactly the TOL set, are they ?

From the QC35 blurb:

But we didn’t stop there. We made them even better, because the Action button lets you adjust your level of noise cancellation between three different levels. And you can set it to the one that feels right for your environment and your music.

https://www.bose.co.nz/en_nz/products/headphones/over_ear_headphones/quietcomfort-35-wireless-ii.html#v=qc35_ii_black

The Bose QC 25 aren't quite the top of their product line; the QC 35 adds wireless operation as an option.

Adjusting the "level of noise cancellation", as described for the Q C35, could also be offered in a "naive" analog implementation, I think: Add the inverted noise signal at your best estimate amplitude for "optimum" noise cancelling, add a bit less of it for "medium" noise cancelling. But apparently Bose -- who tend to come out in reviews as having the most effective noise cancelling -- do something smarter than that, based on active feedback of the noise cancelling result.

[tautech]

Well those [Bose QC 25] exactly the TOL set, are they ?

From the QC35 blurb:

But we didn’t stop there. We made them even better, because the Action button lets you adjust your level of noise cancellation between three different levels. And you can set it to the one that feels right for your environment and your music.

https://www.bose.co.nz/en_nz/products/headphones/over_ear_headphones/quietcomfort-35-wireless-ii.html#v=qc35_ii_black

The Bose QC 25 aren't quite the top of their product line; the QC 35 adds wireless operation as an option.

Adjusting the "level of noise cancellation", as described for the Q C35, could also be offered in a "naive" analog implementation, I think: Add the inverted noise signal at your best estimate amplitude for "optimum" noise cancelling, add a bit less of it for "medium" noise cancelling. But apparently Bose -- who tend to come out in reviews as having the most effective noise cancelling -- do something smarter than that, based on active feedback of the noise cancelling result.

Yet when you look at their aviation headsets they don't seem to offer the same flexibility of settings. 
Maybe aviation noises are 'within' a range they can characterize and apply the right global settings for.

Automatically shapes and equalises incoming signals for enhanced clarity and intelligibility.

https://www.bose.co.nz/en_nz/products/headphones/aviation_headsets/a20-aviation-headset.html#ProductTabs_tab0

[ebastler]

I wonder whether even the small in-ear phones (e.g. Bose QC 20) have room for those error detection mics? @Dave, how about a teardown video?

To answer my own question yet again: Indeed, even the small in-ear ANC phones have two microphones for each ear -- one to detect the incoming environmental noise, and one to monitor the efficiency of the noise cancellation behind the speaker, near the ear. Pretty impressive!

There's a nice sequence of tear-down photos here: https://imgur.com/gallery/OGKO0

[ebastler]

Yet when you look at their aviation headsets they don't seem to offer the same flexibility of settings. 
Maybe aviation noises are 'within' a range they can characterize and apply the right global settings for.

Their latest offering for pilots seems to have very similar functionality to the QC 35 -- including "talk through", selectable levels of noise cancelling, and a Bluetooth option: https://www.bose.com/en_us/products/headphones/aviation_headsets/proflight-aviation-headset.html

(Bluethooth?! Are airline pilots allowed to listen to music or podcasts from their iPhones if nothing interesting is going on?)

[tautech]

FMS looks after their duties once they're properly airborne.
They just need watch for warning lights and the gauges.

(daughter's a Captain)

[InterestedTom]

IMO First step is a good mechanical design, with some degree of passive Noise Rejection. Any electronic filter is then orders of magnitude less complicated, since less cancellation is demanded of it for passable performance.

Having said that, given they can fit Active Noise Cancellation into earphones as well as headphones, it seems the filters work pretty well.

You mentioned something about FFT followed by amplitude adjustment followed by IFFT synthesis, this would be much more computationally intense than a simple digital filter implementation. There would be a strong compromise between having enough FFT points to cover low frequencies and having a high enough sample rate to cover high frequencies. It would also take a pretty fast FPGA/ASIC/DSP to do all that in real time, it would also have to be small and low power, to operate within a battery device.

Look up Digital Signal Processing, a FIR or IIR filter with 3 sets of coefficients for different environments would be very simple to implement, and much less computationally intense than full FFT followed by multiplication for each point in the FFT followed by IFFT.

[djnz]

One way to get rid of the delay is to develop a model for environmental noise, created by constantly sampling ambient sounds with microphones. If you are smart and lucky, you can then predict future noise levels and subtract them in realtime.

[Wolfram]

This TI app note http://www.ti.com/lit/an/spra042/spra042.pdf contains a lot of good info on active noise cancellation methods and their implementation.

[ebastler]

Thank you all for a lot of good input so far.

Looking at wraper's comments, and the TI appnote Wolfram linked to, maybe questions (a) to (c) from my original post above are indeed non-issues: Quite possibly, the feed-forward approach is only used to cancel lower frequencies, where slight delays in generating the inverted waveform can be neglected. (The appnote also describes that the microphone can be placed further upstream, so that the sound propagation to the target gives you some extra processing time. But I don't think that is very significant in the small geometry of headphones.)

So maybe my question (d) is the tricky one to solve for an ANC designer. And it seems that another microphone downstream from the speaker, as mentioned in (e), provides the typical answer: Tune your frequency response actively, based on the error signal of that microphone, so you can react e.g. to the user changing the placement of the headphone over their ears.

[Howardlong]

I wonder whether even the small in-ear phones (e.g. Bose QC 20) have room for those error detection mics? @Dave, how about a teardown video?

They do, and you have to be incredibly careful when repairing them. I accidentslly rolled my chair’s castor over a QC20 earbud once. The bud was understandably deformed, but still worked when noise cancellation was off. With noise cancellation on, not only did the noise cancellation not work at all well, there was also a continual white noise element.

I did manage to repair it up to its original performance, but when trying to tidy up my handiwork, I did a partial disassembly again and was not able to get it working well again. I keep meaning to go back and have another go, but I’m pretty sure the way it’s constructed it’s pretty critical precisely where the component parts sit. There’s no easy way to adjust either, you can only really test them when reassembled.

[InterestedTom]

One way to get rid of the delay is to develop a model for environmental noise, created by constantly sampling ambient sounds with microphones. If you are smart and lucky, you can then predict future noise levels and subtract them in realtime.

Nah... This would only work for synthesising noise. Noise isn't subtractive, it's additive. It might be possible to make the background noise appear less audible by adding noise with a different frequency content to make the cumulative noise seem more psychoacoustically inaudible to a given subset of animals.

I should clarify that in Engineering terms noise usually means a signal which when sampled over a sufficiently long (mathematically speaking infinite) time has a fixed frequency content, it's amplitude at any given time is random but it's amplitude distribution when sampled over a sufficient (again mathematically infinite) length of time is fixed.

Environmental/Ambient Sound is time variant in frequency content and/or amplitude content. Not all Sound is Noise, not all Noise is Sound.