Wave Field Synthesis

• Repository https://github.com/spatialaudio/wfs_chapter_hda
• Authors' versions for the chapters (English, German) on Wave Field Synthesis in
  • Stefan Weinzierl (editor): Handbuch der Audiotechnik, 2nd GER edition, Springer, 2025
  • Stefan Weinzierl (editor): Handbook of Audio Technology, 1st ENG edition, Springer, TBA
  • https://link.springer.com/book/10.1007/978-3-662-60369-7

Abstract

Wave field synthesis (WFS) is a spatial reproduction technique. It involves controlled interference to produce spatially and temporally distinct wavefronts. This requires loudspeaker arrays with very dense loudspeaker spacing and individual signal processing for each loudspeaker. Unlike channel-based reproduction methods, WFS calculates the loudspeaker signals using measurement data or audio objects and their spatio-temporal parameters. WFS is used in loudspeaker-based auralisation, reverberation enhancement, 3D sound reinforcement, audiological research and spatialised audio arts.

Essence of WFS in Graphics

2.5D WFS signal flow for rendering a virtual source with its audio signal a(t) towards the sound pressure field p(x,t).

2.5D WFS prefiltering.

2.5D WFS of a virtual point source: acoustic impulse response (left, top), acoustic transfer function (left, bottom) at probe point (x=0, y=0); and wave front snapshot (right) due to excitation with a 15kHz-low-pass filtered impulse.

2.5D WFS of a virtual point source. Single-frequency soundfield: level (left), snap shot of instantaneous sound pressure (right). Colors as indicated below.

Rendered PDF Files of the Chapter

• author's German version that was submitted to publisher
• author's English version that was submitted to publisher

Zenodo Versions / Snapshots of the Repository with DOI

• https://doi.org/10.5281/zenodo.8060879 (author's German version that was submitted to publisher)
• https://doi.org/10.5281/zenodo.17560617 (author's English version that was submitted to publisher) can be cited as: Schultz, F., Hahn, N., & Spors, S. (2025). Wave Field Synthesis (v0.4). Zenodo. https://doi.org/10.5281/zenodo.17560617

Licenses

• text and graphics under CC BY 4.0 license
• source code under MIT license
• publisher Springer has copyright to their finally edited and authors' approved English / German chapters and their layouts
• we use the violine image from https://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Violin.svg/2048px-Violin.svg.png to create the files python/violin_wfs_ENG.png and python/violin_wfs_DEU.png
• we use the photo fotos/WFS_Array_UniRostockH8_2014.jpg CC BY 4.0 Matthias Geier & Sascha Spors
• all other graphics (as pdf, png, eps, svn, ipe) in this repository are CC BY 4.0 Frank Schultz & Nara Hahn

Reference Implementation of the Simulations

• the reference implementation uses and is double checked against the sfs toolbox (>= 0.6.3)
• Python environment install is straightforward with uv sync using the provided pyproject.toml

Recommended Additional Resources

• The complete basics of wave field synthesis in a nutshell
• Jupyter notebook on 2.5D WFS referencing scheme examples

Authors

• Frank Schultz, https://orcid.org/0000-0002-3010-0294, https://github.com/fs446
• Nara Hahn, https://orcid.org/0000-0003-3564-5864, https://github.com/narahahn
• Sascha Spors, https://orcid.org/0000-0001-7225-9992, https://github.com/spors