Artificial Audio

Theses & Projects

Artificial Reverberation with Feedback Delay Networks

The pyFDN logo
The pyFDN logo

Artificial reverberation adds the sound of a space to a dry recording. It is in every music production, game engine, and virtual reality system, and it has to run in real time at low cost. Since Schroeder’s first digital reverberators in the 1960s [1], the dominant approach has been recursive: a few delay lines that feed back into each other, so that a handful of operations per sample produce a dense, slowly decaying tail [2].

The feedback delay network (FDN) is the general form of this idea [3]. Several delay lines are coupled through a feedback matrix, and filters in the loop set how fast each frequency decays. The theory is now well developed: lossless and allpass feedback matrices [4, 5], accurate reverberation-time control [6], echo density and mixing time [7], and modal analysis [8]. Recently, FDNs have also become differentiable, so their parameters can be learned from measured room impulse responses or tuned for colourless sound [9, 10]. Many classic and modern reverberator designs are still missing from a common, tested implementation where they can be compared and combined.

pyFDN is our open-source Python toolbox for designing, simulating, and analysing FDNs (documentation, tutorial), the successor of the MATLAB FDN Toolbox [12]. It builds on FLAMO [11] for differentiable processing in the time and frequency domain. In this project, you implement a reverberator, analysis method, or visualisation of your choice as a new pyFDN module or example, evaluate it, and contribute it back to the toolbox.

Project ideas

Concrete topics, each with starting literature, are collected in the List of Reverb Projects on GitHub. They include, for example:

  • Classic designs: spring and plate reverbs, zita-rev1, Gerzon’s butterfly matrices, nested allpass reverbs, shimmer.
  • Spatial reverberation: binaural, directional, and multichannel FDNs.
  • Room-acoustic models: scattering delay networks, grouped FDNs for coupled rooms, common-slope reverbs.
  • Time-varying and non-linear FDNs.
  • Analysis and learning: loss functions, echo density, reverb matching to measured impulse responses.
  • Visualisations and interactive apps.

Your own idea is welcome too. The project can be taken as a research project or as a master thesis; we agree on the scope when you start.

Prerequisites

Digital signal processing (filters, z-transform), Python, and interest in reverberation and audio effects. Experience with Git and PyTorch helps.

References

  • [1] Schroeder, M. R. & Logan, B. F. “Colorless” artificial reverberation. IRE Trans. Audio AU-9, 209–214 (1961).
  • [2] Välimäki, V., Parker, J. D., Savioja, L., Smith, J. O. & Abel, J. S. Fifty years of artificial reverberation. IEEE Trans. Audio, Speech, Lang. Process. 20, 1421–1448 (2012).
  • [3] Jot, J.-M. & Chaigne, A. Digital delay networks for designing artificial reverberators. in Proc. 90th AES Conv. (1991).
  • [4] Schlecht, S. J. & Habets, E. A. P. On lossless feedback delay networks. IEEE Trans. Signal Process. 65, 1554–1564 (2017).
  • [5] Schlecht, S. J. Allpass feedback delay networks. IEEE Trans. Signal Process. 69, 1028–1038 (2021).
  • [6] Prawda, K., Välimäki, V. & Schlecht, S. J. Improved reverberation time control for feedback delay networks. in Proc. DAFx (2019).
  • [7] Schlecht, S. J. & Habets, E. A. P. Feedback delay networks: Echo density and mixing time. IEEE/ACM Trans. Audio, Speech, Lang. Process. 25, 374–383 (2017).
  • [8] Schlecht, S. J. & Habets, E. A. P. Modal decomposition of feedback delay networks. IEEE Trans. Signal Process. 67, 5340–5351 (2019).
  • [9] Dal Santo, G., Prawda, K., Schlecht, S. J. & Välimäki, V. Differentiable feedback delay network for colorless reverberation. in Proc. DAFx (2023).
  • [10] Mezza, A. I., Giampiccolo, R., De Sena, E. & Bernardini, A. Data-driven room acoustic modeling via differentiable feedback delay networks with learnable delay lines. EURASIP J. Audio, Speech, Music Process. (2024).
  • [11] Dal Santo, G., De Bortoli, G. M., Prawda, K., Schlecht, S. J. & Välimäki, V. FLAMO: An open-source library for frequency-domain differentiable audio processing. in Proc. IEEE ICASSP (2025).
  • [12] Schlecht, S. J. FDNTB: The feedback delay network toolbox. in Proc. DAFx (2020).

Contact

Prof. Sebastian J. Schlecht (sebastian.schlecht@fau.de).