On inquiry, I was told by technical people (I suspect it is a
near-garage shop operation) at Headsets Inc that their rejection system
is all analog. Being somewhat familiar with analog and digital noise
cancelling systems, I can verify that from the HInc system that I have.
Oddly enough the final performance seems somewhat similar.

It is easy to talk about a 180 degree cancelling pressure waveform
generator (per Roger above), but that is an over-simplification of the
problem that isn't acheiveable from a real control loop stability
standpoint.

Digital systems get around this by a slow optimization in the frequency
domain over a wide (i. e. hi) frequency range at the expense of being
able to cancel random noise, whereas analog does it in the time at the
expense of bandwidth, limiting it to a few hundred Hz, but making
analog better at random uncorrelated noise rejection. The Headsets inc
website posted the rejection capability of their system At low
frequencies it is about as good as the best digital system.

At high frequencies (above say 300 Hz), the passive rejection
capability of a good headset (mine is a David Clark H10-40) is more
than adequate to the task for my ears.

I've been trying to get HI interested in random motorcycle helmet noise
cancellation (generally under 100 Hz) but they don't seem interested -
or they may know why the analog control system can't be made stable.

From my engineering experience, a 300 Hz analog response loop is an
impressive acheivement.