在噪声环境下精准优化混响滤波器，提升音频系统稳定性

Recursion is a fundamental concept in the design of filters and audio systems. In particular, artificial reverberation systems that use delay networks depend on recursive paths to control both echo density and the decay rate of modal components. The differentiable digital signal processing framework has shown promise in automatically tuning recursive and non-recursive elements using gradient-based optimization with perceptually or physically motivated loss functions, such as energy decay or spectrogram differences. These representations are highly sensitive to model mismatches, which can lead to spurious loss minima. In particular, discrepancies in background noise can result in inaccurate attenuation estimates. This paper addresses the problem of tuning recursive attenuation filters of a feedback delay network when targets are noisy. We analyze the loss profile associated with different optimization objectives and propose a method that explicitly models noise, improving the accuracy of the estimated attenuation filters under low signal-to-noise conditions. We demonstrate the effectiveness of the proposed approach through statistical analysis on both synthetic and real target data. Furthermore, we identify the sensitivity of attenuation filter parameters tuning to perturbations in frequency-independent parameters. These findings provide practical guidelines for more robust and reproducible gradient-based optimization of feedback delay networks.