Fourier Series Explorer
Draw custom waveforms and see them decomposed into Fourier series in real time. Visualize how frequencies combine.
About Fourier Series Explorer
Draw a shape on the canvas and watch it instantly decompose into a stack of spinning sine waves. Fourier Series Explorer lets you sketch any waveform — a square wave, a sawtooth, something completely irregular — then shows you the individual frequency components that add together to recreate it. Drag the harmonics, adjust amplitudes, and the reconstruction updates in real time.
It's a genuinely useful tool for anyone working through signal processing concepts or just curious why a clarinet sounds different from a flute playing the same note. The visual feedback makes abstract math tangible: you can see exactly which frequencies contribute the most, and what happens when you strip the higher harmonics away. If you enjoy this kind of interactive education through math visualization, it's a productive corner of the catalog to explore.
Graphing Calculator goes in a different direction — plotting functions rather than decomposing waveforms — but covers similar mathematical ground if you want to keep building intuition. A larger screen helps here because the full waveform canvas and the frequency bar chart are displayed side by side, and they get cramped on small displays.
Look inside
How to use
• Draw waveforms by clicking and dragging your mouse on the left canvas - the Fourier series updates instantly as you draw • Set X-Max to define your signal's period and Y-Max for amplitude range before drawing or using presets • Use preset buttons (Square, Triangle, Sawtooth) to generate classic waveform examples • Plot precise waveforms by entering x,y coordinates in the text area (one point per line) and clicking "Plot from Points" • Adjust the Harmonics slider to see how adding more sine/cosine terms improves the reconstructed wave accuracy • View the frequency spectrum in the bottom chart to see the amplitude of each harmonic component • If the reconstructed wave gets clipped due to high amplitudes, click the "Auto-scale" button to see the full, unclipped waveform • The tool automatically scales axes when plotting points that exceed current X-Max or Y-Max values Goal: Learn how complex periodic signals can be broken down into simple sine and cosine waves through interactive visualization.
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