Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions

Werner KJ, Germain FG, Goldsmith CS. Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions. J Audio Eng Soc. 2021;69(7/8):465-485. doi:10.17743/jaes.2021.0018

@article{Werner2021_21114,
  author = {Werner, Kurt James and Germain, Francois G. and Goldsmith, Cory S.},
  title = {{Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions}},
  journal = {Journal of the Audio Engineering Society},
  volume = {69},
  number = {7/8},
  pages = {465--485},
  year = {2021},
  month = jul,
  publisher = {Audio Engineering Society},
  doi = {10.17743/jaes.2021.0018},
  url = {https://doi.org/10.17743/jaes.2021.0018}
}

TY  - JOUR
TI  - Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions
AU  - Werner, Kurt James
AU  - Germain, Francois G.
AU  - Goldsmith, Cory S.
T2  - Journal of the Audio Engineering Society
J2  - J. Audio Eng. Soc.
VL  - 69
IS  - 7/8
SP  - 465
EP  - 485
PY  - 2021
DA  - 2021/07/06
DO  - 10.17743/jaes.2021.0018
UR  - https://doi.org/10.17743/jaes.2021.0018
PB  - Audio Engineering Society
LA  - en
AB  - We propose time-varying Schroeder allpass filters and Gerzon allpass reverberators that remain energy preserving irrespective of arbitrary variation of their allpass gains or feedback matrices over time. We propose various ways of realizing the unitary matrix involved in the Schroeder structure, based on classic ladder and lattice filters and their generalizations. We show how to construct more elaborate structures including nestings and cascade, giving various strategies for reducing their implementation cost. Extending these algorithms to the multi-input, multi-output case yields time-varying, energy-preserving generalizations of Gerzon’s reverberator, providing a link between Schroeder allpass filters and Schelcht’s recently proposed “Allpass Feedback Delay Networks.” Stability proofs are given for common uses of Schroeder allpass filters, such as inside of Feedback Delay Network reference structures. Finally we give a substantial review of the properties of time-invariant Schroeder allpass filters.
ER  -