Gibbs Phenomenon
is interesting in this aspect. My attempt to nerd snipe the post: As the time duration decreases with more sinusoids detectors will not be able to pick up the complete spike.
This post discussed the Fourier expansion with a finite number of terms. It's true that no matter how many terms you include, there is always the ~9% overshoot. If, however, you actually take the limit of the Fourier series (the limit of infinitely many terms), then the Fourier series of the square wave converges to the square wave at every point (it converges to the midpoint at the jumps).
So if you were able to create a configuration of infinitely many black holes, you could create a perfect square wave signal. Of course, this is physically impossible, but we are not able to create artificial configurations of black holes either.
JulianWgs | 17 hours ago
Gibbs Phenomenon is interesting in this aspect. My attempt to nerd snipe the post: As the time duration decreases with more sinusoids detectors will not be able to pick up the complete spike.
patryk | 13 hours ago
It doesn't have to break the joke! Image is sufficiently imprecise to treat x=0 and so on as y=0 and then we can match square wave perfectly!
thasso | 2 hours ago
This post discussed the Fourier expansion with a finite number of terms. It's true that no matter how many terms you include, there is always the ~9% overshoot. If, however, you actually take the limit of the Fourier series (the limit of infinitely many terms), then the Fourier series of the square wave converges to the square wave at every point (it converges to the midpoint at the jumps).
So if you were able to create a configuration of infinitely many black holes, you could create a perfect square wave signal. Of course, this is physically impossible, but we are not able to create artificial configurations of black holes either.