Infinite sums of sine & cosine waves can represent any periodic function
f(t) =
5
0.80×
1.00×
How it works
Any periodic signal can be decomposed into a (possibly infinite) sum of sines and cosines —
each with its own frequency, amplitude, and phase. The rotating
circles (epicycles) each represent one harmonic. The tip of the last circle traces the
approximated waveform as all circles spin at their respective frequencies.
f(t) = a₀ + Σ [ aₙ cos(nωt) + bₙ sin(nωt) ]
Add more harmonics to watch the approximation sharpen toward the ideal wave — including the
famous Gibbs phenomenon near sharp edges.