Fourier Transforms
Beautiful interactive visual introduction to Fourier transforms with epicycle animations.
About Fourier Transforms
Draw a shape on screen and watch it instantly decompose into spinning circles — each one a single frequency, stacked together to trace your original line. That's the core of Fourier Transforms: an interactive visualization that turns abstract math into something you can feel in your hands. Drag the example waveforms, sketch your own, and see how adding more epicycles gradually sharpens the approximation from a wobbly blob into a crisp outline.
Fourier analysis sits behind audio compression, image processing, and signal filtering, but textbooks rarely show you why it works. This app skips the equations-first approach and lets the geometry do the explaining. If you enjoy this kind of hands-on approach, browse more education apps in the catalog — or try Graphing Calculator to keep exploring math visually.
Works best on a larger screen where you have room to sketch; a mouse or stylus gives you the most control over the shapes you draw.
Look inside
How to use
This is an interactive educational tool that teaches Fourier transforms through visual demonstrations and hands-on activities. • Scroll through the page to read explanations and interact with animated examples • Click play buttons to hear different sound frequencies and wave combinations • Use sliders to adjust the number of sine waves and see how they build up complex patterns • Draw your own waves and shapes in the interactive canvases using your mouse or finger • Watch as your drawings are automatically converted into spinning circles (epicycles) that recreate your drawing • Experiment with the wave-drawing section by clicking and dragging to create custom waveforms • Use the epicycle drawing tool to create any shape and see it decomposed into circular motions The tool demonstrates how complex patterns can be broken down into simple sine waves or spinning circles. Each interactive element updates in real-time as you adjust controls. The goal is to build intuitive understanding of how Fourier transforms work by letting you see and hear the mathematics in action. No prior knowledge of mathematics is required - simply explore each section and experiment with the interactive elements to learn how waves, frequencies, and circular motions relate to each other.
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