提出直接形式数字滤波器的自动微分加速方法，显著提升计算效率。
Accelerating Automatic Differentiation of Direct Form Digital Filters
- 基于闭式反向传播公式，统一计算滤波器及其梯度
- 在GPU上实现1000倍以上速度提升，低阶滤波器比频域方法更快
- 适合需要高效梯度计算的信号处理与深度学习场景
我们提出了直接形式滤波器的通用自动微分框架，得到包含初始条件梯度的闭式反向传播表达式。该表达式可同时表示滤波器计算与梯度推导，并支持并行化。在PyTorch中用C++/CUDA实现，相比原始Python实现至少提速1000倍，且在GPU上始终表现最优。对于实际中常用的低阶滤波器，采用解析梯度的时域滤波方法在速度上优于频域方法。源代码已公开于https://github.com/yoyolicoris/philtorch。
原文摘要 · Abstract (English)
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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