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

2025-09-12

AI Summary

This work addresses the challenge of high-fidelity digital modeling of the analog-level amplifier Teletronix LA-2A. We propose a feedforward differentiable compressor modeling framework based on the Newton–Raphson method. Methodologically, the LA-2A’s core nonlinear dynamics are modeled as a parameterized recursive filter; automatic differentiation combined with GPU-accelerated Hessian computation enables rapid and robust Newton–Raphson convergence. Additionally, we integrate differentiable signal processing with lightweight neural network optimization to enhance modeling accuracy and generalization. Our key contributions are: (i) the first application of second-order optimization to virtual analog audio modeling, significantly improving training efficiency and dynamic response fidelity; and (ii) an open-source implementation deployed in a real-time VST plugin, achieving an exceptional balance among audio quality, latency, and computational resource consumption.

Technology Category

• Machine Learning: Learning on the Edge & Model Compression
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Affective Computing

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Emulate analogue levelling amplifiers digitally
• Optimize compressor parameters via Newton-Raphson method
• Compute Hessian matrix efficiently for training

Innovation

• Newton-Raphson method optimization
• Differentiable digital signal processing
• Parallel recursive filter algorithms