Fractional Fourier Sound Synthesis
🤖 AI Summary
This paper addresses the limited timbral expressivity and dynamic control in conventional audio synthesis, arising from strict temporal–spectral domain separation. We propose a novel alpha-domain sound synthesis paradigm based on the fractional Fourier transform (FrFT). Methodologically, we introduce the first alpha-domain signal modeling framework, leveraging the continuous fractional order α of the FrFT to enable adjustable rotation within the time–frequency plane; synthesis and filtering are directly parameterized in this alpha-domain. This approach overcomes the fixed-window limitation of the short-time Fourier transform (STFT), enabling continuous interpolation and joint manipulation of time–frequency characteristics. Experiments demonstrate that our method generates distinctive timbres, non-stationary dynamic textures, and perceptually smooth time–frequency transitions—effects unattainable with conventional time–frequency methods. The framework provides an interpretable, controllable tool for computer music and acoustic design, backed by a new theoretical foundation for spectral–temporal representation.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Applying Fractional Fourier Transform to sound synthesis
Exploring time-frequency flexibility via fractional order parameters
Enabling novel sound design techniques like alpha-synthesis
Innovation
Methods, ideas, or system contributions that make the work stand out.
FrFT enables continuous time-frequency domain interpolation
Alpha-domain synthesis creates unique timbral characteristics
Alpha-filtering leverages FrFT's rotation properties
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