Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson
  Method
Authors: name: Chin-Yun Yu, name: György Fazekas
Organization: Centre for Digital Music

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.