Fourier Series Simulator

Approximate waves by adding sine harmonics

Wave type

Harmonics

Fourier Series Rules

Square wave	odd sine harmonics: 1/n
Sawtooth wave	all sine harmonics: 1/n
Triangle wave	odd harmonics: 1/n^2

How to Read the Simulator

Increasing harmonics makes the approximation closer to the target wave.
Sharp corners and jumps need many terms to approximate well.
Square waves show visible overshoot near jumps.
Triangle waves converge faster because their coefficients shrink more quickly.

Example: a square wave approximation with 1 term is just a sine wave. With 9, 19, or more harmonics, the curve becomes flatter at the top and steeper near transitions.

Frequently Asked Questions

What is a Fourier series?▼

A Fourier series represents a periodic function as a sum of sine and cosine waves.

What are harmonics?▼

Harmonics are sine or cosine components whose frequencies are integer multiples of the fundamental frequency.

Why does the approximation improve with more terms?▼

Adding more harmonics captures more detail of the target waveform.

What is Gibbs phenomenon?▼

Gibbs phenomenon is the overshoot that appears near jump discontinuities in Fourier approximations.

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