For Researchers · Fourier Series
Fourier Series for a matrix transform
Built for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model. Simulate a matrix transform live below — adjust the inputs and watch it respond, right in your browser.
Fourier Series BuilderLive
synthesize waves from sinusoids
Controls
Add harmonics and watch sine waves sum into a square, sawtooth, or triangle wave — the Fourier series in action.
Presets
Data Inspector
Wavesquare
Harmonics8
Basissine
Governing equation
Reading this result: Reconstructing the square wave from 8 sine harmonics. More harmonics sharpen the reconstruction and pull it closer to the ideal shape. But at each discontinuity the Gibbs phenomenon leaves a persistent ~9% overshoot spike — adding terms only narrows that ripple, it never removes it, no matter how many harmonics you sum.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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Frequently asked questions
- Is this good for researchers?
- Yes — this version of "Fourier Series for a matrix transform" is framed for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.