Série de Fourier — signal carré
A square wave can be built entirely from sine waves, which seems unlikely until you watch it happen. This simulation adds harmonics one at a time and the flat tops emerge from the accumulating curves.
Comment utiliser cette simulation
- Add harmonics one at a time
- Adjust individual harmonic amplitudes
- Compare the sum with the ideal square wave
Ce qu’il faut observer
- Only odd harmonics contribute to a square wave
- The approximation improves quickly at first, then very slowly
- The overshoot at each edge never disappears, only narrows
La physique derrière
Fourier's theorem states that any periodic waveform is a sum of sinusoids at multiples of the fundamental frequency. A square wave needs only the odd harmonics, with amplitudes falling as 1/n. No finite number of terms is ever exact — an overshoot near each edge, the Gibbs phenomenon, persists no matter how many harmonics are added.