运用牛顿-拉弗森法实现模拟电平放大器的声音匹配

摘要

近年来，通过数字信号处理算法实现虚拟模拟建模的自动微分技术日益受到关注。这类算法通常比依赖密集矩阵乘法的黑箱神经网络具有更高的计算效率。由于其可微特性，它们能够与神经网络集成，并利用梯度下降算法进行联合训练，从而构建出更为高效的系统。此外，信号处理算法的参数量远少于神经网络，这使得牛顿-拉夫森方法得以应用。该方法以二次存储为代价，提供了比梯度下降更快且更稳健的收敛速度。本文提出了一种方法，通过使用参数经牛顿-拉夫森方法优化的前馈数字压缩器来模拟模拟电平放大器。我们证明，数字压缩器能够成功逼近目标设备Teletronix LA-2A的行为。文中对计算海森矩阵的不同策略进行了基准测试，并利用递归滤波器的并行算法实现了在现代GPU上的高效训练。最终模型被制作成VST插件，并在https://github.com/aim-qmul/4a2a开源发布。

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.

运用牛顿-拉弗森法实现模拟电平放大器的声音匹配

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

摘要

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