用分数傅里叶变换实现新型声音合成，突破传统时频分析限制
Fractional Fourier Sound Synthesis
- 引入分数阶傅里叶变换，实现时频域连续旋转
- 可在alpha域直接合成声音，生成传统方法无法实现的音色
- 适合音乐创作与声学设计领域探索新声效
本文探索分数傅里叶变换（FrFT）在声音合成中的创新应用，强调其在音频处理中重新定义时频分析的潜力。作为经典傅里叶变换的扩展，FrFT 引入分数阶参数，实现时域与频域之间的连续插值，极大提升信号操控的灵活性。关键在于，FrFT 允许直接在 alpha 域合成声音，为创造前所未有的音色与动态特征提供独特框架。本文深入探讨 FrFT 的数学原理、历史演进及其对复杂音频纹理合成的能力。通过实验分析，展示了 alpha 合成与 alpha 滤波等新技术，利用 FrFT 的时频旋转特性生成创新声学效果。研究结果证实，FrFT 是作曲家、声音设计师及研究人员突破听觉创造力边界的重要工具。
原文摘要 · Abstract (English)
This paper explores the innovative application of the Fractional Fourier Transform (FrFT) in sound synthesis, highlighting its potential to redefine time-frequency analysis in audio processing. As an extension of the classical Fourier Transform, the FrFT introduces fractional order parameters, enabling a continuous interpolation between time and frequency domains and unlocking unprecedented flexibility in signal manipulation. Crucially, the FrFT also opens the possibility of directly synthesizing sounds in the alpha-domain, providing a unique framework for creating timbral and dynamic characteristics unattainable through conventional methods. This work delves into the mathematical principles of the FrFT, its historical evolution, and its capabilities for synthesizing complex audio textures. Through experimental analyses, we showcase novel sound design techniques, such as alpha-synthesis and alpha-filtering, which leverage the FrFT's time-frequency rotation properties to produce innovative sonic results. The findings affirm the FrFT's value as a transformative tool for composers, sound designers, and researchers seeking to push the boundaries of auditory creativity.
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