The Ill-Conditioning Problem in Sound Field Reconstruction

Fazi FM, Nelson PA. The Ill-Conditioning Problem in Sound Field Reconstruction. In: AES Convention 123. Audio Engineering Society; 2007. Paper 7244. Available from: https://aes.org/publications/elibrary-page/?id=14302

@inproceedings{Fazi2007_14302,
  author = {Fazi, Filippo M. and Nelson, Philip A.},
  title = {{The Ill-Conditioning Problem in Sound Field Reconstruction}},
  booktitle = {AES Convention 123},
  note = {Paper 7244},
  year = {2007},
  month = oct,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=14302}
}

TY  - CPAPER
TI  - The Ill-Conditioning Problem in Sound Field Reconstruction
AU  - Fazi, Filippo M.
AU  - Nelson, Philip A.
T2  - AES Convention 123
M1  - Paper 7244
PY  - 2007
DA  - 2007/10/06
UR  - https://aes.org/publications/elibrary-page/?id=14302
PB  - Audio Engineering Society
LA  - en
AB  - A method for the analysis and reconstruction of a three dimensional sound field using an array of microphones and an array of loudspeakers is presented. The criterion used to process the microphone signals and obtain the loudspeakers signals is based on the minimisation of the least-square error between the reconstructed and the original sound field. This approach requires the formulation of an inverse problem that can lead to unstable solutions due to the ill-conditioning of the propagation matrix. The concepts of generalised Fourier transform and singular value decomposition are introduced and applied to the solution of the inverse problem in order to obtain stable solutions and to provide a clear understanding of the regularisation method.
ER  -