Differentiable Attenuation Filters for Feedback Delay Networks

TL;DR

This paper presents a differentiable method for designing scalable, frequency-dependent attenuation filters in Feedback Delay Networks, improving reverberation quality while reducing computational complexity through shared parameters and gradient-based optimization.

Contribution

It introduces a novel, scalable, and fully differentiable filter design approach using SOS IIR filters as parametric equalizers for FDN reverberation systems.

Findings

Achieves state-of-the-art reverberation quality.

Reduces computational cost compared to traditional methods.

Provides a flexible, differentiable filter design framework.

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.