Fourier Series Builder
Fourier’s claim scandalised his colleagues: any periodic signal — even one with corners — is a sum of smooth sines. This builder shows it two ways at once: a chain of rotating circles (epicycles), one per harmonic, whose tip traces the wave; and the partial sum drawn over the target square, sawtooth or triangle wave. Crank up the number of harmonics and the fit sharpens everywhere except the jumps, where the stubborn 9% Gibbs overshoot refuses to die — exactly as the mathematics says it must.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- A square wave needs only odd harmonics with amplitudes 1/n; a sawtooth uses every harmonic.
- The Gibbs overshoot near a jump tends to about 9% of the jump height no matter how many terms you add.
- Smoother signals have faster-decaying coefficients — corners cost you 1/n², jumps only 1/n.
- Runs 100% in your browser — simulations are computed locally on your device.
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