In reply to:

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Take a copy of your regular signal, as seen from your amp, and invert it. Add it to the input from the microphone. You would need to have some kind of adjustment for calibrating the cancellation circuit - perhaps just a amplifier control and calibrating the music level when there is no noise in the car (parked). Might work...

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Might work, but I suspect that there's more to it than that - propogation delays and frequency-domain transfer function will have an effect. If you're smart with the software, though, you can give more credence to the calculation when the music is quiet than when it's loud.

This is something that's been on my wishlist for a while, but I haven't even got around to buying a suitable microphone yet, never mind writing the software...