Interactive Fourier Explorer
Decompose complex periodic waveforms into a sum of simple oscillating sine and cosine waves. Adjust the harmonics and observe how rotating epicycles generate the target function.
f(x) = a0 + ∑
(an cos(nx) + bn sin(nx))
Domain: Time (t)
Points Rendered: 0
Frequency Spectrum
Learn
A Fourier Series expands a periodic function into an infinite sum of sines and cosines. This implies that any complex repeating pattern can be broken down into fundamental, simple oscillations.
Visualized here as connecting rotating circles. Each circle represents one term in the Fourier series. The radius is the amplitude, the rotation speed is the frequency, and adding them vectorially traces the complex shape!
Notice the "wiggles" or "ringing" near sharp corners (like the edges of the Square Wave)? This is the Gibbs phenomenon. Because we use continuous sine waves, they struggle to perfectly replicate instantaneous jumps, resulting in overshoot.