Mathematical Models for Audio Generation and Processing Effects in Interactive Media

This paper provides a systematic review of mathematical models for audio generation and processing effects in interactive media applications. It first analyzes the core challenges of interactive audio in terms of real-time performance, controllability, and adaptability. Building upon this foundation, the paper focuses on dissecting three major technical approaches. Traditional methods, represented by physical modeling and procedural audio, offer computational efficiency and intuitive interactivity. Sample-based synthesis techniques, such as wavetable and granular synthesis, enable rich real-time variations while maintaining sound quality. Cutting-edge deep generative models and neural audio processing models deliver unprecedented generative diversity and audio fidelity, achieving high-level semantic control through conditional generation and latent space manipulation. Current research is driving interactive audio toward real-time, conditional, and semantic capabilities. Future success hinges on balancing high-performance models with stringent real-time and low-resource constraints.