Reproduce “Differentiable All-pole Filters for Time-varying Audio Systems” on OpenResearch
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About this paper
Chin-Yun Yu, Christopher Mitcheltree, Alistair Carson, Stefan Bilbao, Joshua D. Reiss, György Fazekas
A new method provides an exact and efficient backpropagation algorithm for time-varying all-pole filters, overcoming limitations of approximation-based approaches in differentiable digital signal processing. This enables more accurate modeling of dynamic audio systems and ensures consistent performance between training and real-time inference, with speedups of up to 30x.
Key insights
- The recursive nature of all-pole filters can be leveraged to efficiently compute gradients by applying a reversed version of the filter in reverse time, avoiding the deep unrolled graphs of standard automatic differentiation.
- By reparameterizing the relationship between IIR coefficients and the impulse response, exact gradients for time-varying coefficients can be derived without explicitly computing the full impulse response.
- Integrating a high-performance, custom-implemented filter function (e.g., with Numba) as a PyTorch operator allows for seamless and efficient end-to-end differentiable processing of recursive audio components.
Summary by alphaXiv.
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