Abstract
Infinite impulse response filters are an essential building block of many time-varying audio systems, such as audio effects and synthesisers. However, their recursive structure impedes end-to-end training of these systems using automatic differentiation. Although non-recursive filter approximations like frequency sampling and frame-based processing have been proposed and widely used in previous works, they cannot accurately reflect the gradient of the original system. We alleviate this difficulty by re-expressing a time-varying all-pole filter to backpropagate the gradients through itself, so the filter implementation is not bound to the technical limitations of automatic differentiation frameworks. This implementation can be employed within any audio system containing filters with poles for efficient gradient evaluation. We demonstrate its training efficiency and expressive capabilities for modelling real-world dynamic audio systems on a phaser, time-varying subtractive synthesiser, and feed-forward compressor. We make our code available and provide the trained audio effect and synth models in a VST plugin at this https URL.
Abstract (translated)
无限响应滤波器是许多时间变化音频系统（如音频效果和合成器）的基本构建模块。然而，其递归结构阻碍了使用自动微分来训练这些系统。尽管在之前的工作中，已经提出了并广泛使用了非递归滤波器近似，如频率采样和基于帧的处理，但这些滤波器无法准确地反映原始系统的梯度。我们通过重新表示时间变化的全体 pole滤波器来通过反向传播梯度来缓解这个问题，因此滤波器实现不受自动微分框架的技术限制。这个实现可以在包含具有极点的滤波器的任何音频系统中高效地使用。我们在phaser、时间变化的减法合成器和前馈压缩器上展示了其训练效率和表现力，用于建模真实世界动态音频系统。我们将代码公开，可在此链接处下载训练好的音频效果和合成器模型：https://url.com/
URL
https://arxiv.org/abs/2404.07970
