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Unraveling FM Synthesis Through Spectral Analysis and Sound Reconstruction
- Program: Applied Mathematics and Statistics
- Course: Other
- Year: 2025
Project Description:
This project explores the mathematical foundations and perceptual effects of Frequency Modulation (FM) synthesis—a powerful technique used in sound design. Inspired by the classic Yamaha DX7 synthesizer, we reconstruct FM sound generation from first principles, using computational tools to analyze how modulation parameters affect the resulting timbre. By applying the Short-Time Fourier Transform (STFT), we break down audio signals into evolving spectral components, visualizing how simple waveforms combine to create rich, dynamic textures. We also introduce an interactive interface for real-time exploration of spectral features and a novel method for reconstructing sounds from their frequency components. Together, these tools provide fresh insights into FM synthesis and how complex audio structures can emerge from simple mathematical processes. This work bridges applied math, signal processing, and musical acoustics—advancing both our understanding and creative potential in sound design.
Project Photo:
Researcher presenting FM synthesis research at MATRX 2025 Conference, showcasing Dexed FM Synthesizer details and FM algorithm on screen, blending technical analysis and sound design creativity.