Fractional Fourier Sound Synthesis

TL;DR

This paper investigates the use of the Fractional Fourier Transform in sound synthesis, demonstrating its ability to create novel audio textures by interpolating between time and frequency domains, thus expanding sound design possibilities.

Contribution

It introduces the application of the FrFT for direct sound synthesis in the alpha-domain, offering new methods like alpha-synthesis and alpha-filtering for innovative audio creation.

Findings

FrFT enables continuous interpolation between time and frequency domains.

Novel sound design techniques using FrFT produce unique sonic textures.

FrFT proves to be a valuable tool for creative audio synthesis.

Abstract

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.