Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method

Yu CY, Fazekas G. Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method. In: 2025 AES International Conference on Artificial Intelligence and Machine Learning for Audio. Audio Engineering Society; 2025. Paper 2. Available from: https://aes.org/publications/elibrary-page/?id=22991

@inproceedings{Yu2025_22991,
  author = {Yu, Chin-Yun and Fazekas, George},
  title = {{Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method}},
  booktitle = {2025 AES International Conference on Artificial Intelligence and Machine Learning for Audio},
  note = {Paper 2},
  year = {2025},
  month = sep,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=22991}
}

TY  - CPAPER
TI  - Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method
AU  - Yu, Chin-Yun
AU  - Fazekas, George
T2  - 2025 AES International Conference on Artificial Intelligence and Machine Learning for Audio
M1  - Paper 2
PY  - 2025
DA  - 2025/09/02
UR  - https://aes.org/publications/elibrary-page/?id=22991
PB  - Audio Engineering Society
LA  - en
AB  - Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on dense matrix multiplications. Due to their differentiable nature, they can be integrated with neural networks and jointly trained using gradient descent algorithms, resulting in more efficient systems. Furthermore, signal processing algorithms have significantly fewer parameters than neural networks, allowing the application of the Newton-Raphson method. This method offers faster and more robust convergence than gradient descent at the cost of quadratic storage. This paper presents a method to emulate analogue levelling amplifiers using a feed-forward digital compressor with parameters optimised via the Newton-Raphson method. We demonstrate that a digital compressor can successfully approximate the behaviour of our target unit, the Teletronix LA-2A. Different strategies for computing the Hessian matrix are benchmarked. We leverage parallel algorithms for recursive filters to achieve efficient training on modern GPUs. The resulting model is made into a VST plugin and is open-sourced.
ER  -