Fourier Harmonics

Visual mechanical decomposition of square and sawtooth waves into revolving epicyclic phasor circles based on Fourier analysis.

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Harmonic Phasors (N) 7

Fourier series terms

Phasor Rotation Speed 1.2

Fundamental frequency speed

69 chars medium

Analytical Equation

f(t) = \frac{4}{\pi} \sum_{k=1,3,5\dots}^{N} \frac{1}{k} \sin(k \omega t)

Compact Formula

r_k = (4 / kπ) * R, x += r_k cos(k t), y += r_k sin(k t), trace(y)

Renderer Logic

const n = i * 2 + 1;
const radius = baseRadius * (4 / (n * Math.PI));
x += radius * Math.cos(n * t);
y += radius * Math.sin(n * t);

Open in Playground Zero Dependencies • Standalone

#fourier #epicycles #harmonics #signal-processing #waves #synthesis

Author: Math Art Core Target: 60 FPS