Differentiable All-pole Filters for Time-varying Audio Systems

• URL: http://arxiv.org/abs/2404.07970v4
• Date: Sat, 19 Oct 2024 01:25:13 GMT
• Title: Differentiable All-pole Filters for Time-varying Audio Systems
• Authors: Chin-Yun Yu, Christopher Mitcheltree, Alistair Carson, Stefan Bilbao, Joshua D. Reiss, György Fazekas,
• Abstract summary: We re-express a time-varying all-pole filter to backpropagate the gradient through itself. This implementation can be employed within audio systems 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 compressor.
• Score: 9.089836388818808
• License:
• 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 audio systems 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 compressor. We make our code and audio samples available and provide the trained audio effect and synth models in a VST plugin at https://diffapf.github.io/web/.

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