4 ms·
In practice, yes you can only approximate it, because in theory it requires an infinite series of sinusoidal waves. But since maths is all about the theory, Lap
by AceJohnny2 4y ago
In practice, yes you can only approximate it, because in theory it requires an infinite series of sinusoidal waves. But since maths is all about the theory, Laplace's objections were silly.
(though I admit I don't know what the state of acceptance of infinite series was at that time)
Also, it's fine to cut off the infinite series of sinusoidal waves because all physical systems cut off around a given frequency, for example human hearing around ~20kHz.
- armadsen 4y agoAlso, in practice, there's no such thing as a truly sharp corner, which makes sense intuitively based on the math, I think. But real systems have inertia, friction, stray resistance/capacitance/inductance, etc. so you can't have a truly perfect square wave in a physical or electrical system in the real world.
- tuatoru 4y ago* Lagrange's objections
- AceJohnny2 4y agowhoops! thanks. Too late to edit.
- andrepd 4y agoNot quite, that's not the problem. We're in the realm of maths here and therefore of pure abstraction, so that's not the point. Adding terms to the Fourier series of a square wave you have an overshoot that does not converge to zero as the number of terms goes to infinity. This is called the Gibbs phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon