Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson
  Method
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 at https://github.com/aim-qmul/4a2a.
68cb2c245a7803ff3be42cc3
Chin-Yun Yu
claimed_verified
2025-09-18T13:27:30.543Z
621d85a10e35b2fbbf3e6196
https://cdn-avatars.huggingface.co/v1/production/uploads/621d85a10e35b2fbbf3e6196/D6DMntYh-eV5fVef_Mx4Z.png
Chin-Yun Yu
user
yoyolicoris
68cb2c245a7803ff3be42cc4
György Fazekas
Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson
  Method
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 at https://github.com/aim-qmul/4a2a.
A digital compressor is optimized using the Newton-Raphson method to emulate the behavior of an analogue levelling amplifier, demonstrating efficient training and approximation using parallel recursive filters.
automatic differentiation digital signal processing virtual analogue modelling feed-forward digital compressor Newton-Raphson method Hessian matrix recursive filters VST plugin