Three-Dimensional Sound Field Reproduction Using Multiple Circular Loudspeaker Arrays

Three-dimensional spatial sound field reproduction enables enhanced immersive acoustic experience for a listener. Recreating an arbitrary 3-D spatial sound field using a practically realizable array of loudspeakers is a challenging problem in acoustic signal processing. This paper exploits the underlying characteristics of wavefield propagation to devise a strategy for accurate 3-D sound field reproduction inside a 3-D region of interest with practical array geometries. Specifically, we use the properties of the associated Legendre functions and the spherical Hankel functions, which are part of the solution to the wave equation in spherical coordinates, for loudspeaker placement on a set of multiple circular arrays and provide a technique for spherical harmonic mode-selection to control the reproduced sound field. We also analyze the artifacts of spatial aliasing due to the use of discrete loudspeaker arrays in the region of interest. As an illustration, we design a third-order reproduction system to operate at a frequency of 500 Hz with 18 loudspeakers arranged in a practically realizable configuration.

[1]  Heinz Teutsch,et al.  Modal Array Signal Processing: Principles and Applications of Acoustic Wavefield Decomposition , 2007 .

[2]  Yoko Yamakata,et al.  Performance Evaluation of 3D Sound Field Reproduction System Using a Few Loudspeakers and Wave Field Synthesis , 2008, 2008 Second International Symposium on Universal Communication.

[3]  Ramani Duraiswami,et al.  Capture and Recreation of Higher-Order 3D Sound Fields via Reciprocity , 2004, ICAD.

[4]  Sascha Spors,et al.  Analytical driving functions for higher order Ambisonics , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[5]  Rodney A. Kennedy,et al.  Characterization of 3D spatial wireless channels , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[6]  Rozenn Nicol,et al.  3D-Sound Reproduction Over an Extensive Listening Area: A Hybrid Method Derived from Holophony and Ambisonic , 1999 .

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

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

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

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

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

[12]  R. Rabenstein,et al.  The Theory of Wave Field Synthesis Revisited , 2008 .

[13]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[14]  Emmanuel Friot,et al.  Active control of sound inside a sphere via control of the acoustic pressure at the boundary surface , 2005, physics/0507104.

[15]  Jerome Daniel,et al.  Further Study of Sound Field Coding with Higher Order Ambisonics , 2004 .

[16]  Thushara D. Abhayapala,et al.  Spherical Harmonic Analysis of Wavefields Using Multiple Circular Sensor Arrays , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[17]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[18]  F. Bowman,et al.  Introduction to Bessel Functions , 1939 .

[19]  Roland Potthast,et al.  Analogies and differences between three methods for sound field reproduction , 2009 .

[20]  David G. Malham,et al.  3-D Sound Spatialization using Ambisonic Techniques , 1995 .

[21]  H. S. Hall,et al.  Higher Algebra: A Sequel to Elementary Algebra for Schools , 1964 .

[22]  Philip A. Nelson,et al.  Surround System Based on Three-Dimensional Sound Field Reconstruction , 2008 .

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

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

[25]  Walter Kellermann,et al.  Detection and localization of multiple wideband acoustic sources based on wavefield decomposition using spherical apertures , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[26]  D. de Vries,et al.  Wave field synthesis and analysis using array technology , 1999, Proceedings of the 1999 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. WASPAA'99 (Cat. No.99TH8452).

[27]  Thushara D. Abhayapala,et al.  Theory and Design of Soundfield Reproduction Using Continuous Loudspeaker Concept , 2009, IEEE Transactions on Audio, Speech, and Language Processing.

[28]  Stephanie Bertet,et al.  3D Sound Field Recording with Higher Order Ambisonics – Objective Measurements and Validation of a 4th order Spherical Microphone , 2006 .