Look, it seems like you don't really know what ANC is and how it works, but the short awnser is no, processing power of the phone actually doesn't matter in this case, there are a lot of reasons why this won't work, the most important one is latency

Exactly !

I really DO know what ANC is, and how it works. The most simple example being connecting two speakers out of phase; a more complex example being physical lens stabilization on military binoculars, or mechanical sound damping in a handgun suppressor, or hydraulic vibration dampeners on a crankshaft.

So, let’s talk latency: How do ANC ‘phones overcome latency whilst a cellphone would not be able to do so? The ‘phones are tasked with playing an out-of-phase version of ambient noise that is picked up by microphones. What processing power do they possess that a phone could not offer?

Ok, cool, you listed some tech that uses similar technology, but that doesn't mean you have a good understanding on how the tech works. The issue is still latency, you'll need to invert the signal in the time the soundwaves travels between the microphone and the speaker, when you try to send that singal to your phone, convert it there and send it back to your headphone, by the time it gets played that soundwave is long past the speaker

Yes. Cool. Audio phase cancellation. Known about since the 30’s. How do my neckbuds deal with the latency issue that my phone would be unable to handle?

Is it the real-time software processing versus hardware-based that is the problem? I use an old PC that can de-click and de-hiss records in real time with zero delay between the processed and unprocessed sound.

Nerd fact: simply mixing to mono can get rid of a lot of surface noise on an LP through phase cancellation. I used that method in the 90s before DCART existed. My software now does it through DSP, though.

Mate, i already told you, processing power isn't the issue

You gotta get the bloody microphone signal into your audio cable (ADC) then send it through your cable, process it, send it back to your headphone (DAC) and then play it, if you look up the time a typical ADC and DAC needs, (don't expect anything fancy or super fast in a generic pair of headphones or phone) you'll be already above the ~0.05ms it takes for the soundwave to travel from your microphone to the speaker, no chance to cancel out anything, especially considering the phone doesn't know how far the mic and drivers are appart and what ADC your headphones are using

I told you, the biggest problem is latency, not processing power, i don't know why that's so hard to understand

Then how does the bloody signal get picked up by my neckbuds’ mic, processed through the ADC, processed by the DSP, processed through the DAC, sent through the amp, and into the drivers without said latency issues?

[removed]

As you probably know, ANC headphones aren't the best sounding devices out there, they are very likely trading processing time for speed to achieve desired results, the DAC and amp in a pair of ANC headphones are nothing like the one in a regular phone or headphone, but if you are interested in a DIY project I found this PDF: https://www.google.com /url?q=https://courses.physics.illinois.edu/phys406/sp2017/Student_Projects/Spring12/Danylo_Hirnyj_P406_Project_Report_Sp12.pdf&sa=U&ved=2ahUKEwj2jvSVrLv7AhWoXvEDHU24AGQQFnoECAQQAg&usg=AOvVaw05PJIiwqh6tUowxQ6KcHvZ Of a guy attempting to build a pair himself (Remove the space in the URL, it's before the / after www.google.com, Reddit blocked the original link)

The same way audio interfaces can offer "zero-latency" monitoring that would typically suffer from lag if the input needed to be routed to the phone/tablet/pc and back out.

Besides latency, I think the software would also need to know the frequency response of the headphones in order to send a correct inverted signal to the output?

I'd expect dedicated ANC headphones have their ANC tuned to their specific audio characteristics, and even more advanced implementations have dedicated mics inside the earcups to monitor the process in realtime?

ANC is hardware reliant. Because you don’t just need a microphone. You need a properly positioned microphone, with a set pickup pattern, with almost immediate processing. In a nutshell, no