Earlier quoted context omitted.
That sounds reasonable. Let's do the math your way in both directions: 1) Assuming system-level model 10,000 microphones * 8 kilosamples per second = 800 megasamples per second. NVidia Tesla does 100 teraflops. I get about 125,000 FLOPS per sample. That feels adequate to me! 2) One filter per microphone per passenger. We need to divide by 250. 500 FLOPS per sample per passenger. That's more than enough for a very fan…
Right, and now you've achieved the same noise cancelling performance... That off the shelf noise canceling headphones achieve (1 kHz) without putting 10000 microphones on the plane. Again assuming this all works, which is a massive if. Look, this isn't practical.
The answer to that might be right now (we couldn't do it before, and we probably can today) or it might be in a decade. But electronics will keep falling in price. 10,000 microphones * $5 per microphone+electronics = $50k.
The advantages of cancelling an entire wavefront go well beyond passenger comfort too. Industrial noise cancelling systems are more about equipment life than about employee comfort. I had laptop screws unscrew on airplanes before, due to vibration. If planes need less maintenance as a result of active vibration reduction throughout the airplane, you'll make up that $50k virtually overnight.
As a footnote, the crazy part here isn't the 10,000 microphones, but the speaker-at-every-seat part. You'd almost certainly want both the microphones and speakers in the skin of the airplane. But that's a story for another day.