> on the hypothesis that we have a pure, periodic signal in there
That pure sine wouldn't generate any artefacts. It would result in a 200Hz output from the AI if it throws the phase information out. You wouldn't hear a difference unless its an (aptly so called) complex signal. Eg. 200 and 201 Hz layered is an impure signal with a period below 1Hz, far outside the scope. Eventually the signals will cancel out completely. [1]
The important point is, I think, that FFT doesn't simply look at the offset aka phase. Rather, 201 Hz looks like a 200 Hz that is moving. So it encodes phase-shift in the delta of the offset between two windows. For a sum of 200 and 201 Hz it has to assume that the magnitude is also changing, which I find entirely counterintuitive.
From the mathematical perspective, this seems like a borring homework, far detached from accoustics. So, I don't know. The funny thing is that rotation is very real in the movement of strings. If the orbit in one point is elliptic, that's like two sinusoids at different magnitudes offset by some 90 degree, in a simplified model. But it has nearly infinite coupled points along its axis. As they exite each other, and each point has a different distance to the receiver, that's where phase shift happens.
> If you look here at the definition of the ω (omega) parameter
I wasn't going to make drone, but I will take a look.
That pure sine wouldn't generate any artefacts. It would result in a 200Hz output from the AI if it throws the phase information out. You wouldn't hear a difference unless its an (aptly so called) complex signal. Eg. 200 and 201 Hz layered is an impure signal with a period below 1Hz, far outside the scope. Eventually the signals will cancel out completely. [1]
The important point is, I think, that FFT doesn't simply look at the offset aka phase. Rather, 201 Hz looks like a 200 Hz that is moving. So it encodes phase-shift in the delta of the offset between two windows. For a sum of 200 and 201 Hz it has to assume that the magnitude is also changing, which I find entirely counterintuitive.
From the mathematical perspective, this seems like a borring homework, far detached from accoustics. So, I don't know. The funny thing is that rotation is very real in the movement of strings. If the orbit in one point is elliptic, that's like two sinusoids at different magnitudes offset by some 90 degree, in a simplified model. But it has nearly infinite coupled points along its axis. As they exite each other, and each point has a different distance to the receiver, that's where phase shift happens.
> If you look here at the definition of the ω (omega) parameter
I wasn't going to make drone, but I will take a look.
1: https://graphtoy.com/?f1(x,t)=100*sin(x)&v1=true&f2(x,t)=100...