Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method
Chin-Yun Yu, György Fazekas
2025-09-17
Summary
This paper explores a new way to recreate the sound of classic analog audio equipment, specifically a leveling amplifier called the Teletronix LA-2A, using computer algorithms.
What's the problem?
Traditionally, creating realistic virtual versions of analog audio gear relied on either complex 'black box' neural networks which require a lot of computing power, or simpler digital signal processing algorithms that weren't easily adjustable to perfectly match the original sound. Neural networks have many adjustable settings, but are slow, while older digital methods were fast but inflexible. The goal was to find a method that was both efficient *and* accurate.
What's the solution?
The researchers used a digital compressor, a type of signal processing algorithm, and a powerful optimization technique called the Newton-Raphson method to fine-tune its settings. Instead of just tweaking settings randomly, this method uses mathematical calculations to quickly find the best settings to mimic the LA-2A's behavior. They also figured out how to speed up these calculations using the parallel processing capabilities of modern graphics cards (GPUs). Finally, they packaged their work into a plugin anyone can use.
Why it matters?
This work is important because it offers a more efficient and potentially more accurate way to model analog audio effects. By combining the speed of signal processing with the precision of advanced optimization, it could lead to better-sounding virtual instruments and effects plugins that don't require as much computing power. The open-source nature of the project also allows others to build upon and improve their work.
Abstract
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.