[ghusbands]

You're simply wrong, here. Take a single sinusoid and do that, sure. Take a large number of sinusoids of different frequencies, as all music and public noise is, and invert/offset, and you get everything from double amplitude to zero amplitude. None of these simplistic mental models of noise cancellation will help.

[avianlyric]

Sure, but show me how you get significant frequency shifting, or injection of frequency components greater than found in the two source signals. That’s the topic of discussion, not amplitude changes.

[ghusbands]

There's no mention of frequency shifting or anything like it in the parent post. For amplification of certain frequencies in a signal via simplistic noise cancellation, just take a combination of a sine wave at 10kHz and a sine wave at 1kHz, offset it by 0.00005s (call it signal processing delay) and subtract it from the original. The 1kHz signal is basically (noise-)cancelled and the 10kHz signal is doubled in strength.

Not that any of this is relevant to the original problem.

[avianlyric]

From OP:

> the cancellation is not perfect and what I am actually getting into the ear is the residual high frequency noise, which may in fact be quite dangerous.

From GP:

> I can see quite clearly that the high frequency noise happens when you subtract two images, one of which is shifted by half-pixel for instance. What you are left with is the edges (high frequency) of the image.

Show me the part where the word “amplitude” appears in any parent post.

Additionally as mentioned in parent posts, noise cancelling headphone run a low pass filter over the input to the ANC system, specifically because achieving good alignment between your ANC signal and original signal is basically impossible at wave lengths shorter as you can’t know the exactly which direction the original signal came from (direct perpendicular to the head, or at a close tangential angle), and thus can’t compensate for the offset needed to ensure the two signals arrive at eardrum at the right time.

[ghusbands]

Ah, you're assuming that everyone agrees that ANC always uses an early low-pass filter, and hence there'd be no high frequencies in the noise-cancellation signal. Makes sense.

However, I don't agree that ANC always uses a low-pass filter, and it seems from kalal's followup that they are also talking about the using the full original signal. So the two of us were not talking about introducing high frequencies but about somehow enhancing the high frequencies already present, and that's what the figures I gave above are for. So we've been talking across each other. I apologise for my part in that.

("Amplitude" was a simple technical term to replace woolly terms that were being used, just as you are the first in the parent-chain to say "low pass filter".)