Gradient-Based Optimization of Modulation Effects

Carson A, Wright A, Bilbao S. Gradient-Based Optimization of Modulation Effects. J Audio Eng Soc. 2026;74(7/8):533-543. doi:10.17743/jaes.2026.0273

@article{Carson2026_23385,
  author = {Carson, Alistair and Wright, Alec and Bilbao, Stefan},
  title = {{Gradient-Based Optimization of Modulation Effects}},
  journal = {Journal of the Audio Engineering Society},
  volume = {74},
  number = {7/8},
  pages = {533--543},
  year = {2026},
  month = jul,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2026.0273},
  url = {https://doi.org/10.17743/jaes.2026.0273}
}

TY  - JOUR
TI  - Gradient-Based Optimization of Modulation Effects
AU  - Carson, Alistair
AU  - Wright, Alec
AU  - Bilbao, Stefan
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 74
IS  - 7/8
SP  - 533
EP  - 543
PY  - 2026
DA  - 2026/07/08
DO  - 10.17743/jaes.2026.0273
UR  - https://doi.org/10.17743/jaes.2026.0273
PB  - Audio Engineering Society
LA  - en
AB  - Modulation effects, such as phasers, flangers, and chorus effects, are heavily used in conjunction with the electric guitar. Machine learning–based emulation of analog modulation units has been investigated in recent years, but most methods have either been limited to one class of effect or suffer from a high computational cost or latency compared with canonical digital implementations. This article builds on previous work and presents a framework for modeling flanger, chorus, and phaser effects based on differentiable digital signal processing. The model is trained in the time-frequency domain, but at inference, it operates in the time domain requiring zero latency. The challenges associated with gradient-based optimization of such effects are investigated, and it is shown that low-frequency weighting of loss functions avoids convergence to local minima when learning delay times. It is shown that when trained against analog effects units, sound output from the model is in some cases perceptually indistinguishable from the reference, but challenges still remain for effects with long delay times and feedback.
ER  -