Differentiable Attenuation Filters for Feedback Delay Networks

Abstract

We introduce a novel method for designing attenuation filters in digital audio reverberation systems based on Feedback Delay Networks (FDNs). Our approach uses Second Order Sections (SOS) of Infinite Impulse Response (IIR) filters arranged as parametric equalizers (PEQ), enabling fine control over frequency-dependent reverberation decay. Unlike traditional graphic equalizer designs, which require numerous filters per delay line, we propose a scalable solution where the number of filters can be adjusted. The frequency, gain, and quality factor (Q) parameters are shared parameters across delay lines and only the gain is adjusted based on delay length. This design not only reduces the number of optimization parameters, but also remains fully differentiable and compatible with gradient-based learning frameworks. Leveraging principles of analog filter design, our method allows for efficient and accurate filter fitting using supervised learning. Our method delivers a flexible and differentiable design, achieving state-of-the-art performance while significantly reducing computational cost.