Reproducing Sound Fields Using MIMO Acoustic Channel Inversion

Sound fields are essentially band-limited phenomena, both temporally and spatially. This implies that a spatially sampled sound field respecting the Nyquist criterion is effectively equivalent to its continuous original. We describe Sound Field Reconstruction (SFR)---a technique that uses the previously stated observation to express the reproduction of a continuous sound field as an inversion of the discrete acoustic channel from a loudspeaker array to a grid of control points. The acoustic channel is inverted using truncated singular value decomposition (SVD) in order to provide optimal sound field reproduction subject to a limited effort constraint. Additionally, a detailed procedure for obtaining loudspeaker driving signals that involves selection of active loudspeakers, coverage of the listening area with control points, and frequency domain FIR filter design is described. Extensive simulations comparing SFR with Wave Field Synthesis show that on average, SFR provides higher sound field reproduction accuracy.

[1]  E. W. Stuart,et al.  Application of Curved Arrays in Wave Field Synthesis , 1996 .

[2]  E. Williams,et al.  Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography , 1999 .

[3]  Philippe-Aubert Gauthier,et al.  Adaptive Wave Field Synthesis for Sound Field Reproduction: Theory, Experiments, and Future Perspectives , 2007 .

[4]  J. Blauert.  Spatial Hearing: The Psychophysics of Human Sound Localization , 1983 .

[5]  Etienne Corteel,et al.  Wave Field Synthesis Rendering with Increased Aliasing Frequency , 2008 .

[6]  Christof Faller,et al.  Sound Field Reconstruction: An Improved Approach for Wave Field Synthesis , 2009 .

[7]  O. Kirkeby,et al.  Reproduction of plane wave sound fields , 1993 .

[8]  P. S. Gaskell,et al.  Quadraphony: Developments in matrix H decoding , 1977 .

[9]  Sascha Spors,et al.  Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[10]  Gene H. Golub,et al.  Calculating the singular values and pseudo-inverse of a matrix , 2007, Milestones in Matrix Computation.

[11]  Christof Faller,et al.  Designing Practical Filters For Sound Field Reconstruction , 2009 .

[12]  E. Verheijen.  Sound reproduction by wave field synthesis , 1998 .

[13]  Philip A. Nelson,et al.  Active Control of Sound , 1992 .

[14]  Etienne Corteel.  Synthesis of Directional Sources Using Wave Field Synthesis, Possibilities, and Limitations , 2007, EURASIP J. Adv. Signal Process..

[15]  Michael J. Gerzon.  Periphony: With-Height Sound Reproduction , 1973 .

[16]  Alan D. Blumlein,et al.  British Patent Specification 394,325 (Improvements in and relating to Sound-transmission, Sound-recording and Sound-reproducing Systems) , 1958 .

[17]  Etienne Corteel,et al.  Equalization in an extended area using multichannel inversion and wave field synthesis , 2006 .

[18]  Michael A. Gerzon,et al.  Practical Periphony: The Reproduction of Full-Sphere Sound , 1980 .

[19]  Kevin D. Donohue,et al.  Virtual Sound Source Rendering Using a Multipole-Expansion and Method-of-Moments Approach , 2008 .

[20]  Duane H. Cooper,et al.  Discrete-Matrix Multichannel Stereo , 1972 .

[21]  J. Blauert,et al.  Group delay distortions in electroacoustical systems , 1978 .

[22]  Hareo Hamada,et al.  Fast deconvolution of multichannel systems using regularization , 1998, IEEE Trans. Speech Audio Process..

[23]  S. Spors.  Extension of an Analytic Secondary Source Selection Criterion for Wave Field Synthesis , 2007 .

[24]  Brian C. J. Moore,et al.  Discrimination of Group Delay in Clicklike Signals Presented via Headphones and Loudspeakers , 2005 .

[25]  Jerome Daniel,et al.  Further Investigations of High-Order Ambisonics and Wavefield Synthesis for Holophonic Sound Imaging , 2003 .

[26]  T. Ajdler,et al.  The Plenacoustic Function and Its Sampling , 2006, IEEE Transactions on Signal Processing.

[27]  Jeffery S. Bamford,et al.  Ambisonic Sound for Us , 1995 .

[28]  Diemer de Vries.  Sound reinforcement by wavefield synthesis : Adaptation of the synthesis operator to the loudspeaker directivity characteristics , 1996 .

[29]  A. J. Berkhout,et al.  A Holographic Approach to Acoustic Control , 1988 .

[30]  A. J. Berkhout,et al.  Wave Front Synthesis: A New Direction in Electroacoustics , 1992 .

[31]  A. Berkhout,et al.  Acoustic control by wave field synthesis , 1993 .