Making Math Visual and Interactive

About
Harmonic Wave Studio

A powerful tool for visualizing and understanding Fourier series, making complex mathematical concepts accessible to everyone.

Why We Built This

Fourier series and harmonic analysis are fundamental concepts in mathematics, physics, and engineering. They explain how complex signals can be broken down into simple sine and cosine waves, powering everything from music compression to medical imaging.

However, traditional teaching methods often struggle to convey the beauty and intuition behind these concepts. Students are presented with formulas and equations, but rarely get to see how epicycles actually construct complex waveforms in real-time.

We created Harmonic Wave Studio to bridge this gap—to make abstract mathematics tangible, interactive, and beautiful.

Who Benefits?

Students

Learn Fourier series, signal processing, and frequency analysis through interactive visualization. See formulas come to life and build intuition for complex concepts.

Educators

Create engaging demonstrations for your classes. Show students how epicycles construct waveforms, apply filters, and analyze frequency spectra in real-time.

Engineers

Rapidly prototype signal processing pipelines, test filter designs, and visualize frequency domain transformations without writing code.

Enthusiasts

Explore the beauty of mathematics and create stunning visualizations. Share your creations with the community and discover new patterns.

What We've Built

Real-time epicycle visualization with interactive controls
Fast Fourier Transform (FFT) analysis and frequency spectrum visualization
Digital filters: Low-pass, High-pass, Band-pass, and Notch filters
Signal decomposition showing individual harmonic components
Preset waveforms: Square, Sawtooth, Triangle, and more
Drawing mode: Create custom waveforms with your mouse
Project export/import as JSON files
Signal data export as CSV for further analysis
Visualization export as PNG images
Real-time noise simulation and filtering
Multiple trail tracking for complex visualizations
Graph visibility controls for focused analysis

Future Plans

We're constantly working to improve Harmonic Wave Studio and add new features. Here's what's on our roadmap:

Audio Integration

Generate and playback audio from your waveforms, turning visual patterns into sound.

3D Visualizations

Explore epicycles and waveforms in three-dimensional space for even more stunning visuals.

Collaborative Features

Share projects in real-time with others, perfect for remote teaching and collaboration.

Advanced Signal Processing

Wavelet transforms, time-frequency analysis, and more advanced DSP tools.

Mobile Apps

Native iOS and Android apps for learning on the go.

Educational Curriculum

Step-by-step tutorials and lessons for students at all levels.

Ready to Explore?

Start creating beautiful harmonic visualizations today.