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Differentiable Attenuation Filters for Feedback Delay Networks

Ilias Ibnyahya, Joshua D. Reiss

TL;DR

The paper tackles differentiable attenuation filtering in FDN-based reverberators by replacing fixed GEQs with a scalable, differentiable Parametric Equalizer built from Second-Order Sections. Attenuation across delay lines shares a common spectral shape with line-length dependent gain scaling, enabling a compact parameterization and gradient-based optimization via target $T_{60}(f)$. Experiments on 1000 RIRs show that 12-band PEQ can match TSAF (31 bands) accuracy while using substantially fewer operations (about $38\%$) and a similar parameter count, demonstrating strong efficiency gains. This work enables efficient end-to-end training of differentiable FDNs suitable for real-time and embedded deployment, with clear paths for full FDN integration and coefficient-based representations.

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.

Differentiable Attenuation Filters for Feedback Delay Networks

TL;DR

The paper tackles differentiable attenuation filtering in FDN-based reverberators by replacing fixed GEQs with a scalable, differentiable Parametric Equalizer built from Second-Order Sections. Attenuation across delay lines shares a common spectral shape with line-length dependent gain scaling, enabling a compact parameterization and gradient-based optimization via target . Experiments on 1000 RIRs show that 12-band PEQ can match TSAF (31 bands) accuracy while using substantially fewer operations (about ) and a similar parameter count, demonstrating strong efficiency gains. This work enables efficient end-to-end training of differentiable FDNs suitable for real-time and embedded deployment, with clear paths for full FDN integration and coefficient-based representations.

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.

Paper Structure

This paper contains 8 sections, 14 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. METHOD
  3. Parametric Equalizer Design
  4. Parameter Optimization
  5. Results
  6. Reverberation Time Evaluation
  7. Attenuation Filter Magnitude Accuracy
  8. Conclusions

Figures (3)

  • Figure 1: Recursive filter design with an N-band parametric equalizer.
  • Figure 2: Reverberation time relative error of three different PEQ designs applied to a 1000 RIR reverberation time measurements dataset with a distribution of different delay lengths.
  • Figure 3: Magnitude response accuracy for different PEQ designs based on the dataset median reverberation time at each frequency.