Erthiox Labs - Fourier Series & Wave Sandbox

Fourier Harmonics Builder Spinning epicycles trace

music_note Trigger Audio Synthesis below to hear the harmonic waves

Target Waveform

Harmonic Coefficients

Number of Harmonics (N) 4

Signal Gain (Amplitude) 1.0

Audio Frequency (Hz)

Fundamental Pitch 220 Hz

Web Audio Synth

Fourier Series Formula f(t) = ∑ sin(n·ω·t) / n

Theory: Fourier Harmonics

Fourier's Theorem states that any periodic function can be represented as an infinite sum of simple sine and cosine waves (harmonics). Each harmonic has a frequency that is an integer multiple of the fundamental frequency, and a specific amplitude. Adding these together synthesizes the target shape.

Interactive Lab Tasks

Task 1: Square Wave Harmonics
Select Square Wave preset. Slide the Harmonics Count slider (N) from 1 to 50 and watch the waves' sharp corners form. Task 2: Wave Timbre
Click 'Hear Synthesized Wave' in the Synthesizer tab. Compare the audio sound of a Square wave with a Sine wave to hear the differences in brightness. Task 3: Synthesis Gain
Increase Signal Gain (Amplitude) in the Harmonics tab and observe the larger size of the spinning epicycles (circles).