Fractional Fourier Sound Synthesis

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.

A Statistics-Driven Differentiable Approach for Sound Texture Synthesis and Analysis

In this work, we introduce TexStat, a novel loss function specifically designed for the analysis and synthesis of texture sounds characterized by stochastic structure and perceptual stationarity. Drawing inspiration from the statistical and perceptual framework of McDermott and Simoncelli, TexStat identifies similarities between signals belonging to the same texture category without relying on temporal structure. We also propose using TexStat as a validation metric alongside Frechet Audio Distances (FAD) to evaluate texture sound synthesis models. In addition to TexStat, we present TexEnv, an efficient, lightweight and differentiable texture sound synthesizer that generates audio by imposing amplitude envelopes on filtered noise. We further integrate these components into TexDSP, a DDSP-inspired generative model tailored for texture sounds. Through extensive experiments across various texture sound types, we demonstrate that TexStat is perceptually meaningful, time-invariant, and robust to noise, features that make it effective both as a loss function for generative tasks and as a validation metric. All tools and code are provided as open-source contributions and our PyTorch implementations are efficient, differentiable, and highly configurable, enabling its use in both generative tasks and as a perceptually grounded evaluation metric.