How do noise cancelling headphones work?

A microphone picks up the sound around you, and a chip plays it back through the speaker flipped, so its peaks meet the noise's troughs and the two cancel. An adaptive filter keeps tuning that anti-noise to make what reaches your ear as quiet as it can.

How does AirPods noise cancelling work?

AirPods Pro use an outward-facing microphone to detect the sound around you and an inward-facing one that listens toward your ear for whatever noise remains. Apple says the cancelling continuously adapts 200 times per second.

Why can I still hear voices with noise cancelling on?

Cancelling works best on low, steady sounds such as engine hum, below about 1 kHz. Voices are higher and never repeat, so the anti-noise can't predict them. In the model, a voice gets through at 139% of its power while the hum drops to under 1%. Sony's manual says the same of its headphones.

What's the difference between active and passive noise cancelling?

Passive isolation is the seal: ear cups and tips that block sound physically. Active cancelling adds anti-noise from the speaker and works best on low sounds, below about 1 kHz, where it complements the ear cups. Noise cancelling headphones use both.

Live model · Noise-cancelling headphones

How Noise-Cancelling Headphones Actually Work

Noise cancelling headphones hear the noise with a microphone and play it back flipped, so the two cancel at your ear. A small adaptive filter keeps adjusting that anti-noise to make what reaches your ear quieter. It works best on steady, low sounds like an engine's hum, which repeat and can be predicted. Voices get through.

An adaptive filter against an engine hum

The outer microphone hears an engine hum at 100, 200 and 300 Hz, a faint hiss and, at 200 ms, a voice. Sound reaches your ear 2 ms after the microphone; the chip takes 4 ms to answer. The filter starts with all 12 weights at zero, so at first it plays nothing.

StopLMS adaptive filter

Chip delay, msStep sizeSeed

CH2 Anti-noise, and the voice
CH4 Noise, and the hum

Watch the Python behind this model run, line by line

How to read the stage

The left chart is the noise reaching your ear and the anti-noise the speaker plays; the right chart is their sum, what you hear. The filter starts silent. By 80 ms the hum is down to 4.0% of its power, and by 400 ms to 0.64%, 22 dB quieter. At 200 ms a voice arrives, and 139% of its power gets through: the anti-noise does nothing for it.

How the filter learns

The filter is 12 weights, one for each of the microphone's recent samples, and the anti-noise is their weighted sum. After every sample, each weight takes a small step in whichever direction would have made what you heard quieter. That rule is the least mean squares algorithm Widrow and Hoff published in 1960. Too big a step overshoots and blows up: try a step of 1.

Why the voice gets through

Here sound reaches your ear 2 ms after the outer microphone, and the chip takes 4 ms to answer. So the anti-noise has to be a prediction: easy for a hum that repeats every 10 ms, impossible for a voice that never repeats. Make the chip faster than the head start, 1 ms, and the filter learns to copy the microphone, flipped. Then only 18% of the voice's power gets through.

A chip faster than the sound

The outer microphone hears an engine hum at 100, 200 and 300 Hz, a faint hiss and, at 200 ms, a voice. Sound reaches your ear 2 ms after the microphone; the chip takes 1 ms to answer. The filter starts with all 12 weights at zero, so at first it plays nothing.

StopLMS adaptive filter

Chip delay, msStep sizeSeed

CH2 Anti-noise, and the voice
CH4 Noise, and the hum

Watch the Python behind this model run, line by line

What real headphones do

AirPods Pro pair an outward-facing microphone that hears the world with an inward-facing one that listens toward the ear, and Apple says the cancelling adapts 200 times per second. Real cancelling works best below about 1 kHz: Sony's manual calls it effective for airplanes, trains and air conditioning and less so for voices. The ear cups block higher sounds on their own.

What the model leaves out

The model runs at 1,000 samples a second with a 2 ms head start. In an earbud the outer microphone sits centimeters from the eardrum, a distance sound crosses in a fraction of a millisecond, so real chips work far faster. The path from speaker to ear is a pure delay here, where real systems must measure it. And one microphone stands in for the inner and outer pair real earbuds combine.

Questions

How do noise cancelling headphones work?: A microphone picks up the sound around you, and a chip plays it back through the speaker flipped, so its peaks meet the noise's troughs and the two cancel. An adaptive filter keeps tuning that anti-noise to make what reaches your ear as quiet as it can.
How does AirPods noise cancelling work?: AirPods Pro use an outward-facing microphone to detect the sound around you and an inward-facing one that listens toward your ear for whatever noise remains. Apple says the cancelling continuously adapts 200 times per second.
Why can I still hear voices with noise cancelling on?: Cancelling works best on low, steady sounds such as engine hum, below about 1 kHz. Voices are higher and never repeat, so the anti-noise can't predict them. In the model, a voice gets through at 139% of its power while the hum drops to under 1%. Sony's manual says the same of its headphones.
What's the difference between active and passive noise cancelling?: Passive isolation is the seal: ear cups and tips that block sound physically. Active cancelling adds anti-noise from the speaker and works best on low sounds, below about 1 kHz, where it complements the ear cups. Noise cancelling headphones use both.