Real-Time Fractional Fourier Sound Synthesis and Processing

Gutiérrez E, Haki B, Long CS, Font F, Serra X, Cádiz RF. Real-Time Fractional Fourier Sound Synthesis and Processing. J Audio Eng Soc. 2026;74(10):714-730. doi:10.17743/jaes.2026.0286

@article{Gutierrez2026_23445,
  author = {Gutiérrez, Esteban and Haki, Behzad and Long, Carlos Sing and Font, Frederic and Serra, Xavier and Cádiz, Rodrigo F.},
  title = {{Real-Time Fractional Fourier Sound Synthesis and Processing}},
  journal = {Journal of the Audio Engineering Society},
  volume = {74},
  number = {10},
  pages = {714--730},
  year = {2026},
  month = oct,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2026.0286},
  url = {https://doi.org/10.17743/jaes.2026.0286}
}

TY  - JOUR
TI  - Real-Time Fractional Fourier Sound Synthesis and Processing
AU  - Gutiérrez, Esteban
AU  - Haki, Behzad
AU  - Long, Carlos Sing
AU  - Font, Frederic
AU  - Serra, Xavier
AU  - Cádiz, Rodrigo F.
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 74
IS  - 10
SP  - 714
EP  - 730
PY  - 2026
DA  - 2026/10/09
DO  - 10.17743/jaes.2026.0286
UR  - https://doi.org/10.17743/jaes.2026.0286
PB  - Audio Engineering Society
LA  - en
AB  - The fractional Fourier transform (FRFT) extends the classical FT by introducing a continuous order parameter that interpolates between time and frequency representations. While widely used for audio analysis, enhancement, and compression, its potential as a direct basis for sound synthesis, particularly in real-time, remains largely unexplored. This paper presents a real-time framework for sound synthesis and processing in the intermediate time–frequency representation defined by the FRFT, based on a computationally efficient approximation suitable for low-latency applications. The authors introduce several novel techniques, including α-processing, α-synthesis, α-convolution, α-filters, and α-ring modulation, which exploit the FRFT’s geometric interpretation as a rotation in the time–frequency plane. To facilitate direct auditory exploration, the authors formalize the real FRFT and analyze its mathematical and sonic properties. Validation shows that the implementation preserves the key properties of the FRFT with high numerical accuracy, while performance benchmarks confirm its real-time viability. Through sound examples and spectrographic analyses, it is demonstrated that processing in this intermediate representation enables novel timbral structures, dynamic frequency modulations, and hybrid behaviors unattainable with conventional Fourier-based methods. These results position the FRFT and real FRFT as practical and expressive tools for interactive sound synthesis and design.
ER  -