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KU. JA. Werner, FR. G.. Germain, and CO. S.. Goldsmith, "Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions," J. Audio Eng. Soc., vol. 69, no. 7/8, pp. 465-485, (2021 July.). doi: https://doi.org/10.17743/jaes.2021.0018 KU. JA. Werner, FR. G.. Germain, and CO. S.. Goldsmith, "Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions," J. Audio Eng. Soc., vol. 69 Issue 7/8 pp. 465-485, (2021 July.). doi: https://doi.org/10.17743/jaes.2021.0018
Abstract: 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.

@article{werner2021energy-preserving,
author={werner, kurt james and germain, francois g. and goldsmith, cory s.},
journal={journal of the audio engineering society},
title={energy-preserving time-varying schroeder allpass filters and multichannel extensions},
year={2021},
volume={69},
number={7/8},
pages={465-485},
doi={https://doi.org/10.17743/jaes.2021.0018},
month={july},} @article{werner2021energy-preserving,
author={werner, kurt james and germain, francois g. and goldsmith, cory s.},
journal={journal of the audio engineering society},
title={energy-preserving time-varying schroeder allpass filters and multichannel extensions},
year={2021},
volume={69},
number={7/8},
pages={465-485},
doi={https://doi.org/10.17743/jaes.2021.0018},
month={july},
abstract={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.},}

TY - paper
TI - Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions
SP - 465 EP - 485
AU - Werner, Kurt James
AU - Germain, Francois G.
AU - Goldsmith, Cory S.
PY - 2021
JO - Journal of the Audio Engineering Society
IS - 7/8
VO - 69
VL - 69
Y1 - July 2021 TY - paper
TI - Energy-Preserving Time-Varying Schroeder Allpass Filters and Multichannel Extensions
SP - 465 EP - 485
AU - Werner, Kurt James
AU - Germain, Francois G.
AU - Goldsmith, Cory S.
PY - 2021
JO - Journal of the Audio Engineering Society
IS - 7/8
VO - 69
VL - 69
Y1 - July 2021
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.