Mode-matching based multizone reproduction has been mainly focused on a purely two-dimensional (2D) theory, where infinite-long 2D secondary sources are assumed for 2D multizone reproduction. Its extension to the three-dimensional (3D) case requires more secondary sources and a higher computational complexity. This work investigates a more practical setup to use 3D sound sources as secondary sources for multizone reproduction in a 2D horizontal plane, i.e., 2.5D multizone reproduction. A weighted mode-matching approach is proposed to solve the dimensionality mismatch between the 2D desired sound field and 3D reproduced sound field. The weighting is based on an integral of Bessel-spherical harmonic modes over the entire control region. A detailed analysis of the weighting function is provided to show that the proposed method controls all the reproduction modes present on the 2D plane to minimize the reproduction error. The method is validated in both simulation-based and hardware-based experiments. The results demonstrate that in comparison with the conventional sectorial mode-matching method, the proposed approach can achieve more accurate reproduction over a wide frequency range and a large control region.
References
1.
T.
Betlehem
, W.
Zhang
, M. A.
Poletti
, and T. D.
Abhayapala
, “Personal sound zones: Delivering interface-free audio to multiple listeners
,” IEEE Signal Proc. Mag.
32
(2
), 81
–91
(2015
).2.
W.
Zhang
, P.
Samarasinghe
, H.
Chen
, and T. D.
Abhayapala
, “Surround by sound: A review of spatial audio recording and reproduction
,” Appl. Sci.
7
(5
), 532
(2017
).3.
J.
Cheer
and S. J.
Elliott
, “Design and implementation of a personal audio system in a car cabin
,” in Proceedings of the International Conference on Acoustics (ICA)
, Vancouver, Canada (May 26–31, 2013
), p. 055009
.4.
S. J.
Elliott
and M.
Jones
, “An active headrest for personal audio
,” J. Acoust. Soc. Am.
119
(5
), 2702
–2709
(2006
).5.
H.
So
and J. W.
Choi
, “Subband optimization and filtering technique for practical personal audio systems
,” in Proceedings of the IEEE ICASSP
, Brighton, UK (May 12–17, 2019
), pp. 8494
–8498
.6.
M.
Buerger
, C.
Hofmann
, and W.
Kellermann
, “Broadband multizone sound rendering by jointly optimizing the sound pressure and particle velocity
,” J. Acoust. Soc. Am.
143
(3
), 1477
–1490
(2018
).7.
J.-H.
Chang
and F.
Jacobsen
, “Sound field control with a circular double-layer array of loudspeakers
,” J. Acoust. Soc. Am.
131
(6
), 4518
–4525
(2012
).8.
J. W.
Choi
and Y. H.
Kim
, “Generation of an acoustically bright zone with an illuminated region using multiple sources
,” J. Acoust. Soc. Am.
111
(4
), 1695
–1700
(2002
).9.
Y.
Cai
, M.
Wu
, L.
Liu
, and J.
Yang
, “Time-domain acoustic contrast control design with response differential constraint in personal audio systems
,” J. Acoust. Soc. Am.
135
(6
), EL252
–EL257
(2014
).10.
Q.
Feng
, F.
Yang
, and J.
Yang
, “Time-domain sound field reproduction using the group lasso
,” J. Acoust. Soc. Am.
143
(2
), EL55
–EL60
(2018
).11.
M. F. S.
Gálvez
, S. J.
Elliott
, and J.
Cheer
, “Time domain optimization of filters used in a loudspeaker array for personal audio
,” IEEE Trans. Audio Speech Lang. Process.
23
(11
), 1869
–1878
(2015
).12.
Z.
Han
, M.
Wu
, Q.
Zhu
, and J.
Yang
, “Two-dimensional multizone sound field reproduction using a wave-domain method
,” J. Acoust. Soc. Am.
144
(3
), EL185
–EL190
(2018
).13.
M. A.
Poletti
and F. M.
Fazi
, “An approach to generating two zones of silence with application to personal sound systems
,” J. Acoust. Soc. Am.
137
(2
), 598
–605
(2015
).14.
Y. J.
Wu
and T. D.
Abhayapala
, “Spatial multizone soundfield reproduction: Theory and design
,” IEEE Trans. Audio Speech Lang. Process.
19
(6
), 1711
–1720
(2011
).15.
W.
Jin
and W. B.
Kleijn
, “Theory and design of multizone soundfield reproduction using sparse methods
,” IEEE Trans. Audio Speech Lang. Process.
23
(12
), 2343
–2355
(2015
).16.
M. A.
Poletti
and F. M.
Fazi
, “Generation of half-space sound fields with application to personal sound systems
,” J. Acoust. Soc. Am.
139
(3
), 1294
–1302
(2016
).17.
N.
Ueno
, S.
Koyama
, and H.
Saruwatari
, “Three-dimensional sound field reproduction based on weighted mode-matching method
,” IEEE Trans. Audio Speech Lang. Process.
27
(12
), 1852
–1867
(2019
).18.
J.
Ahrens
and S.
Spors
, “An analytical approach to sound field reproduction using circular and spherical loudspeaker distributions
,” Acta Acust. united Ac.
94
(6
), 988
–999
(2008
).19.
S.
Spors
, V.
Kuscher
, and J.
Ahrens
, “Efficient realization of model-based rendering for 2.5-dimensional near-field compensated higher order ambisonics
,” in Proceedings of the IEEE WASPAA
, New Paltz, NY (October 16–19, 2011
), pp. 61
–64
.20.
F.
Winter
, J.
Ahrens
, and S.
Spors
, “On analytic methods for 2.5-D local sound field synthesis using circular distributions of secondary sources
,” IEEE Trans. Audio Speech Lang. Process.
24
(5
), 914
–926
(2016
).21.
W.
Zhang
and T. D.
Abhayapala
, “2.5 D sound field reproduction in higher order ambisonics
,” in Proceedings of IEEE IWAENC
, Juan-les-Pins, France (September 8–11, 2014
), pp. 342
–346
.22.
T.
Okamoto
, “2.5D higher order ambisonics for a sound field described by angular spectrum coefficients
,” in Proceedings of the IEEE ICASSP
, Shanghai, China (March 20–25, 2016
), pp. 326
–330
.23.
T.
Okamoto
, “Analytical approach to 2.5D sound field control using a circular double-layer array of fixed-directivity loudspeakers
,” in Proceeding of the IEEE ICASSP
, New Orleans, LA (March 5–9, 2017
), pp. 91
–95
.24.
T.
Okamoto
, “Horizontal 3D sound field recording and 2.5D synthesis with omni-directional circular arrays
,” in Proceedings of the IEEE ICASSP
, Brighton, UK (May 12–17, 2019
), pp. 960
–964
.25.
W.
Zhang
, J.
Zhang
, T. D.
Abhayapala
, and L.
Zhang
, “2.5 D multizone reproduction using weighted mode matching
,” in Proceedings of the IEEE ICASSP
, Calgary, Canada (April 15–20, 2018
), pp. 476
-480
.26.
E. G.
Williams
, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
(Academic Press
, New York
, 1999
), Chap. 4, pp. 115
–148
.27.
R. A.
Kennedy
, P.
Sadeghi
, T. D.
Abhayapala
, and H. M.
Jones
, “Intrinsic limits of dimensionality and richness in random multipath fields
,” IEEE Trans. Signal Process.
55
(6
), 2542
–2556
(2007
).28.
P. A.
Martin
, Multiple Scattering: Interaction of Time-Harmonic Waves With N Obstacles
(Cambridge University Press
, Cambridge, UK
, 2006
), Chaps. 2–3, pp. 29
–121
.29.
W.
Zhang
, T. D.
Abhayapala
, T.
Betlehem
, and F. M.
Fazi
, “Analysis and control of multi-zone sound field reproduction using modal-domain approach
,” J. Acoust. Soc. Am.
140
(3
), 2134
–2144
(2016
).30.
T.
Betlehem
and P. D.
Teal
, “A constrained optimization approach for multi-zone surround sound
,” in Proceedings of the IEEE ICASSP
, Prague, Czech Republic (May 22–27, 2011
), pp. 437
–440
.31.
Z.
Luo
, W.
Ma
, A. M.
So
, Y.
Ye
, and S.
Zhang
, “Semidefinite relaxation of quadratic optimization problems
,” IEEE Signal Proc. Mag.
27
(3
), 20
–34
(2010
).32.
T.
Betlehem
and T. D.
Abhayapala
, “Theory and design of sound field reproduction in reverberant rooms
,” J. Acoust. Soc. Am.
117
(4
), 2100
–2111
(2005
).33.
T. D.
Abhayapala
and A.
Gupta
, “Spherical harmonic analysis of wavefields using multiple circular sensor arrays
,” IEEE Trans. Audio Speech Lang. Process.
18
(6
), 1655
–1666
(2010
).34.
M.
Abramowitz
and I. A.
Stegun
, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
(National Bureau of Standards
, New York
, 1970
), Chap. 8, p. 334
.35.
M. A.
Poletti
, T.
Betlehem
, and T. D.
Abhayapala
, “Analysis of 2D sound reproduction with fixed-directivity loudspeakers
,” in Proceedings IEEE ICASSP
, Kyoto, Japan (March 25–30, 2012
), pp. 377
–380
.36.
J. B.
Allen
and D. A.
Berkley
, “Image method for efficiently simulating small-room acoustics
,” J. Acoust. Soc. Am.
65
(4
), 943
–950
(1979
).37.
A.
Farina
, A.
Capra
, L.
Chiesi
, and L.
Scopece
, “A spherical microphone array for synthesizing virtual directive microphones in live broadcasting and in post production
,” in Proceedings of the 40th Audio Engineering Society (AES) Conference
, Tokyo, Japan (October 8–10, 2010
), pp. 1
–11
.38.
Y.
Hu
, P. N.
Samarasinghe
, G.
Dickins
, and T. D.
Abhayapala
, “Modeling the interior response of real loudspeakers with finite measurements
,” in Proceeding of the IEEE IWAENC
, Tokyo, Japan (September 17
–20
, 2018
), pp. 16
–20.39.
M.
Binelli
, A.
Venturi
, A.
Amendola
, and A.
Farina
, “Experimental analysis of spatial properties of the sound field inside a car employing a spherical microphone array
,” in Proceedings of the 130th Audio Engineering Society (AES) Conference
, London, UK (May 13–16, 2011
), pp. 1
–8
.40.
Y.
Huang
and D. P.
Palomar
, “Rank-constrained separable semidefinite programming with applications to optimal beamforming
,” IEEE Trans. Signal Process.
58
(2
), 664
–678
(2009
).41.
P. N.
Samarasinghe
, T. D.
Abhayapala
, and M. A.
Poletti
, “3D spatial soundfield recording over large regions
,” in Proceedings of the IEEE IWAENC
, Aachen, Germany (September 4–6, 2012
), pp. 1
–4
.42.
P. N.
Samarasinghe
, T. D.
Abhayapala
, and M. A.
Poletti
, “Wavefield analysis over large areas using distributed higher order microphones
,” IEEE Trans. Audio Speech Lang. Process.
22
(3
), 647
–658
(2014
).© 2020 Acoustical Society of America.
2020
Acoustical Society of America
You do not currently have access to this content.