Sound Field Reproduction With Energy Constraint on Loudspeaker Weights

Audio rendering problems are not always well-posed. An approach is devised for solving ill-posed sound field reproduction problems using regularization, where the Tikhonov parameter is chosen by upper bounding the summed square of the loudspeaker weights. The method ensures that the sound in the room remains at reasonable levels.

[1]  E. Gilbert,et al.  Optimum design of directive antenna arrays subject to random variations , 1955 .

[2]  Philip A. Nelson,et al.  Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods , 2003 .

[3]  Mark A. Poletti.  Robust Two-Dimensional Surround Sound Reproduction for Nonuniform Loudspeaker Layouts , 2007 .

[4]  Henry Cox,et al.  Practical supergain , 1986, IEEE Trans. Acoust. Speech Signal Process..

[5]  Cheng-Shang Chang.  Calculus , 2020, Bicycle or Unicycle?.

[6]  G. Deschamps,et al.  Antenna synthesis and solution of inverse problems by regularization methods , 1972 .

[7]  Terence Betlehem,et al.  Theory and design of sound field reproduction in reverberant rooms. , 2005, The Journal of the Acoustical Society of America.

[8]  Finn Jacobsen,et al.  Effort variation regularization in sound field reproduction. , 2010, The Journal of the Acoustical Society of America.

[9]  Mark A. Poletti,et al.  Three-Dimensional Surround Sound Systems Based on Spherical Harmonics , 2005 .

[10]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  P. Hansen.  The discrete picard condition for discrete ill-posed problems , 1990 .

[13]  Terence Betlehem,et al.  A constrained optimization approach for multi-zone surround sound , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[14]  Felipe Orduña-Bustamante,et al.  Multi-Channel Signal Processing Techniques in the Reproduction of Sound , 1992 .

[15]  P. Nelson,et al.  Sound-field reproduction systems using fixed-directivity loudspeakers. , 2010, The Journal of the Acoustical Society of America.

[16]  Philip A. Nelson,et al.  Inverse Filter of Sound Reproduction Systems Using Regularization , 1997 .

[17]  Philip A. Nelson,et al.  The Ill-Conditioning Problem in Sound Field Reconstruction , 2007 .

[18]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

[19]  Terence Betlehem,et al.  A Directional Loudspeaker Array for Surround Sound in Reverberant Rooms , 2010 .

[20]  Thushara D. Abhayapala,et al.  Reproduction of a plane-wave sound field using an array of loudspeakers , 2001, IEEE Trans. Speech Audio Process..

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

[22]  Philippe-Aubert Gauthier,et al.  Beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array , 2011 .