Differentiable All-pole Filters for Time-varying Audio Systems
This work addresses a bottleneck for audio engineers and researchers in developing trainable audio effects and synthesizers, representing an incremental improvement over existing approximations.
The authors tackled the problem of training time-varying audio systems with infinite impulse response filters end-to-end using automatic differentiation, by developing a differentiable all-pole filter that backpropagates gradients accurately, resulting in efficient training and expressive modeling of real-world systems like phasers and compressors.
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/.