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I doubt that there are analog-digital, digital-analog converters and an FFT module in there. I would have assumed that there's only some analog circuit. You don't even need spectral analysis. It just needs to invert the amplitude and delay the output for those 60 microseconds, right? This would also make the problems of spikes and Fourier transforms go away.

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Sadly, both of you are quite wrong. ANC can easily cancel wideband sudden sounds. It may have problems at very high frequencies due to frame sizes and required group delay precision. Computing FFT or even more complex transforms with very low latency is possible, as is combining time domain and frequency domain processing. You cannot do analogue ANC at high frequencies, as the internal reflections in the headphone/ear system ruin it, while a digital system can measure these and respond well enough while not damaging the sound. Plus it is very hard to represent psychoacoustics without digital processing and those help preserve sound quality immensely.

Thanks for that. I wouldn't have expected it to be practical to have such low latency FFTs.

Thanks for the explanation!

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