用牛顿-拉夫森法优化数字压缩器，精准复刻经典LA-2A模拟音色。
Sound Matching an Analogue Levelling Amplifier Using the Newton-Raphson Method
- 通过前馈数字压缩器结合牛顿-拉夫森法优化参数，实现模拟放大器建模。
- 在真实硬件（LA-2A）上测试，模型能准确还原其非线性响应特性。
- 支持现代GPU高效训练，已开源为VST插件，适合音频工程与虚拟乐器开发者。
基于自动微分的数字信号处理算法在虚拟模拟建模中日益流行。这类算法计算效率高于依赖密集矩阵乘法的黑箱神经网络，且因其可微特性可与神经网络联合训练，提升系统效率。此外，信号处理算法参数远少于神经网络，适用于牛顿-拉夫森方法。该方法虽需二次存储空间，但收敛更快更鲁棒。本文提出一种使用前馈数字压缩器并以牛顿-拉夫森法优化参数来模拟模拟音量控制放大器的方法。实验表明，该数字压缩器能有效逼近目标设备——Teletronix LA-2A的行为。文中对比了多种海森矩阵计算策略，并利用递归滤波的并行算法实现在现代GPU上的高效训练。最终模型已封装为VST插件并开源至https://github.com/aim-qmul/4a2a。
原文摘要 · Abstract (English)
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.
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