Learning Recursive Attenuation Filters Under Noisy Conditions

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 both recursive and non-recursive elements given a target room impulse response. This is done by applying gradient descent to loss functions based on energy-decay or spectrogram differences. However, these representations are highly sensitive to background noise, which is ubiquitous in real measurements, producing spurious loss minima and leading to incorrect attenuation. This paper addresses the problem of tuning recursive attenuation filters of a feedback delay network when targets are noisy. We examine the loss landscape associated with different optimization objectives and propose a method that ensures correct minima under low signal-to-noise conditions. We demonstrate the effectiveness of the proposed approach through statistical analysis on 80 individual optimization examples. The results reveal that explicitly modeling the noise restores correct minima. 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.