Making-Scientific-Visualizations-with-the-Omniacs
🎵 Fourier Transform in Motion | Animated Signal Decomposition with Manim
This project animates how complex signals are built from — and decomposed into — sine waves using the Fourier Transform. Created with Manim, it shows how waveforms evolve in both the time and frequency domains.
🔊 What It Shows
- 📈 Composite Wave Construction: Left panel shows a wave built from sine components
- 🎨 Sine Component Display: Right panel plots each sine wave by frequency and amplitude
- 📉 Wave Breakdown: Each sine is subtracted to break the wave down
- 📊 Frequency Histogram: A spectrum appears showing amplitude vs frequency
🧠 Educational Concepts
- Fourier series and signal composition
- Amplitude spectrum representation
- Time-domain ↔ Frequency-domain duality
- Signal decomposition and reconstruction
🎨 Visual Breakdown
| Panel | Visualizes |
|---|---|
| Left | Composite wave (time-domain) |
| Right (initial) | Individual sine waves added to the signal |
| Right (final) | Histogram of frequencies (spectrum) |
| Color Coding | Each sine wave has a unique color |
📦 Requirements
- Python 3.8+
- Manim Community Edition
- NumPy
pip install manim numpy
▶️ How to Run
manim -pql Fourier_Transform.py FourierTransformVisualization
Use -qh for high-resolution rendering. 📁 Files
Fourier_Transform.py — Main Manim animation script
README.md — This documentation
🎓 Perfect For
Signal processing education
Understanding frequency decomposition
STEM visual learning
DSP, audio, and math teaching material
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