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arXiv · 2511.14390

Accelerating Automatic Differentiation of Direct Form Digital Filters

Chin-Yun Yu·György Fazekas
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Abstract

We introduce a general formulation for automatic differentiation through direct form filters, yielding a closed-form backpropagation that includes initial condition gradients. The result is a single expression that can represent both the filter and its gradients computation while supporting parallelism. C++/CUDA implementations in PyTorch achieve at least 1000x speedup over naive Python implementations and consistently run fastest on the GPU. For the low-order filters commonly used in practice, exact time-domain filtering with analytical gradients outperforms the frequency-domain method in terms of speed. The source code is available at https://github.com/yoyolicoris/philtorch.

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Chin-Yun Yu, György Fazekas. 2025-11-18. Accelerating Automatic Differentiation of Direct Form Digital Filters. https://arxiv.org/abs/2511.14390

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