Active Noise Cancellation

An ANC headset fights noise with anti-noise: an inverted copy of the incoming sound, played so its peaks land on the noise’s troughs. The catch is timing — the anti-noise has to arrive at your eardrum at the same instant. Every microsecond the mic→chip→speaker loop takes becomes a phase error that grows with frequency, and past a point the “anti-noise” stops cancelling and starts adding. Drag the latency slider and watch the cancellation collapse.

Noise & controller

Noise

Frequency 200 Hz Tone 2 700 Hz

Loop latency 500 µs · 24 smp

Block size

latency of one DSP block @ 48 kHz — watch the band collapse as blocks grow

Anti-noise gain ×1.00 · floor −∞

Loop latency — the time the system takes to respond: reference mic → ADC → processing → DAC → speaker. Anti-noise gain — how loud the inverted copy is played; it should sit at ×1.00 to exactly match the noise (any mismatch leaves a floor of |1−g|). Cancellation only works below f ≈ 1/(6·Δt), so killing noise up to ~1 kHz needs under ~170 µs — which is why ANC leans on analog or per-sample processing rather than large DSP blocks.

The acoustic path

signal flow

The noise travels left→right toward your ear. The reference mic catches it on the way in, giving the controller a head-start — the sound’s travel time between the mics (d/c ≈ 0.23 ms) — to compute the anti-noise the speaker plays. The error mic at the ear reports the leftover residual so the filter can adapt. The latency slider above is the electronic loop delay; what actually matters is whatever timing error is left after that head-start.

Waveforms at the eardrum

time domain

Noise Anti-noise (inverted + delayed) Residual (what you hear)

Cancellation spectrum

attenuation vs frequency

The curve is the controller’s transfer function: how much it cuts (below 0 dB, green) or boosts (above 0 dB, red) each frequency, for the current latency and gain. Dots mark the tones you’ve set.

Result

At the tone

— dB

primary frequency

Overall

— dB

power-weighted

Cancellation band

—

helps below ≈ 1/(6·Δt)

Effective latency

—

after head-start

What you're looking at

Anti-noise is just the noise flipped upside down. Where a peak meets a trough the air pressure cancels — but only if the two arrive at the same instant. A fixed loop delay Δt spoils that alignment.
The delay becomes a phase error that grows with frequency: φ = 360° · f · Δt. Just 1 ms of latency is already a full 180° at 500 Hz — there the anti-noise lands exactly in phase and adds +6 dB instead of cancelling.
With matched gain the residual is 2·sin(π f Δt) of the original. You only get real attenuation below f ≈ 1/(6Δt) — that’s your cancellation band. Slide the latency up and watch the green band shrink toward zero.
Timing isn’t enough — amplitude has to match too. An anti-noise gain that’s off by a factor g leaves a floor of |1−g| no matter how perfect the timing (±10% → only −20 dB).
This is why ANC owns low-frequency rumble — jet cabins, engines, HVAC — and ignores hiss, and why the latency budget is brutal: a single 64-sample block at 48 kHz is already 1.3 ms.
Feedforward placement buys time: a reference mic a few centimetres upstream gives the controller an acoustic head-start, so part of the loop delay is “free” and the band widens. Feedback ANC has no look-ahead, so its delay bites in full. Toggle the two and watch the band move.