The Anti-Phase Trick

Noise-cancelling headphones contain tiny external microphones that pick up ambient sound. A digital signal processor (DSP) analyzes the incoming noise in real time and generates an anti-phase wave, a copy of the noise flipped upside down. Peaks become troughs, troughs become peaks. This inverted signal plays through the speaker along with your music. When the original noise reaches your ear, it meets its mirror image and the two cancel out, often cutting background noise by 20 to 30 decibels. The whole process must happen in microseconds. Any delay, and the cancelling wave falls out of alignment.