My background is in image processing and 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. The same applies to 1D in my opinion. For this reason I am not convinced (1) is actually true. The argument about lack of low frequency is interesting, who knows what is happening there indeed.
Images processing and traditional 1D signal processing are not directly comparable, especially when dealing with analogue signals. You can’t have a true “hard edge” in an analogue 1D signal, because it not physically possible to record or reproduce, so you’re always dealing with sinusoids.
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.
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.
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.
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.
> 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.
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".)
> high frequency noise happens when you subtract two images, one of which is shifted by half-pixel
> 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.
Yes, that would be correct, under the assumption of a lowpass filter. As I've just mentioned elsewhere in the thread, though, I don't think kalal accepted that there was a lowpass filter involved, and even stated such, indirectly, and without that it's easy to have a delayed subtraction that amplifies higher frequencies, as in the image example kalal gave.
