If you take a sinusoids, invert it, slightly offset it, and combine them. You get a smaller signal always, unless you’re delay is larger then 90°.
I would recommend playing with some audio signals in an online simulator and see what you get, you realise that your 2D intuition does not apply well to analogue 1D signals. The strict digital nature of image processing done on a computer creates the possibility of results not easily possible when working on analogue signal. After all you can one pixel on a screen at max brightness, and it’s neighbour completely of, but it’s impossible to recreate a similar hard edge with an audio signal because it would require the speaker to be capable of infinite speed and acceleration.
Not that any of this is relevant to the original problem.
> 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.
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".)
> What you are left with is the edges (high frequency)
So you subtract a slightly phase shifted high frequency signal, you're left with a high frequency signal that may be amplified at the edges depending on your phase shift. Nothing surprising here?
The question is can you create a high frequency residual by subtracting a lowpass filtered (gaussian blur?) image? I don't think so. You're just left with whatever high frequencies you had but you aren't creating any new ones.