Simulated room impulse responses have been proven to be both useful and indispensable for comprehensive testing of acoustic signal processing algorithms while controlling parameters such as the reverberation time, room dimensions, and source–array distance. In this work, a method is proposed for simulating the room impulse responses between a sound source and the microphones positioned on a spherical array. The method takes into account specular reflections of the source by employing the well-known image method, and scattering from the rigid sphere by employing spherical harmonic decomposition. Pseudocode for the proposed method is provided, taking into account various optimizations to reduce the computational complexity. The magnitude and phase errors that result from the finite order spherical harmonic decomposition are analyzed and general guidelines for the order selection are provided. Three examples are presented: an analysis of a diffuse reverberant sound field, a study of binaural cues in the presence of reverberation, and an illustration of the algorithm’s use as a mouth simulator.
REFERENCES
1.
J. B.
Allen
and D. A.
Berkley
, “Image method for efficiently simulating small-room acoustics
,” J. Acoust. Soc. Am.
65
, 943
–950
(1979
).2.
P. M.
Peterson
, “Simulating the response of multiple microphones to a single acoustic source in a reverberant room
,” J. Acoust. Soc. Am.
80
, 1527
–1529
(1986
).3.
E.
Lehmann
and A.
Johansson
, “Diffuse reverberation model for efficient image-source simulation of room impulse responses
,” IEEE Trans. Audio, Speech, Lang. Process.
18
, 1429
–1439
(2010
).4.
T. D.
Abhayapala
and D. B.
Ward
, “Theory and design of high order sound field microphones using spherical microphone array
,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2002
), Vol. 2
, pp. 1949
–1952
.5.
J.
Meyer
and G.
Elko
, “A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield
,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2002
), Vol. 2
, pp. 1781
–1784
.6.
B.
Rafaely
, “Plane-wave decomposition of the pressure on a sphere by spherical convolution
,” J. Acoust. Soc. Am.
116
, 2149
–2157
(2004
).7.
N.
Gumerov
and R.
Duraiswami
, “Modeling the effect of a nearby boundary on the HRTF
,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2001
), Vol. 5
, pp. 3337
–3340
.8.
T.
Betlehem
and M. A.
Poletti
, “Sound field reproduction around a scatterer in reverberation
,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2009
), pp. 89
–92
.9.
D. P.
Jarrett
, “Spherical microphone array impulse response (SMIR) generator
,” http://www.ee.ic.ac.uk/sap/smirgen/.10.
D. P.
Jarrett
, E. A. P.
Habets
, M. R. P.
Thomas
, and P. A. Naylor, “Simulating room impulse responses for spherical microphone arrays
,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
(2011
), pp. 129
–132
.11.
This expression assumes the sign convention commonly used in physics/acoustics, whereby the temporal Fourier transform is defined as in order to eliminate the e−iωt term in the time-harmonic solution to the wave equation, as in Refs. 14 and 16. The formulas in this paper are the complex conjugates of those found in other papers which use the opposite sign convention.
12.
Some texts (Ref. 19) refer to the scattering effect as diffraction, although Morse and Ingard note that “When the scattering object is large compared with the wavelength of the scattered sound, we usually say the sound is reflected and diffracted, rather than scattered” (Ref. 14), therefore, in the case of spherical microphone arrays (particularly rigid ones, which tend to be relatively small for practical reasons), scattering is possibly the more appropriate term.
13.
N. A.
Logan
, “Survey of some early studies of the scattering of plane waves by a sphere
,” Proc. IEEE
53
, 773
–785
(1965
).14.
P. M.
Morse
and K. U.
Ingard
, Theoretical Acoustics, International Series in Pure and Applied Physics
(McGraw-Hill
, New York
, 1968
), p. 927
.15.
D. L.
Sengupta
, “The sphere,”
in Electromagnetic and Acoustic Scattering by Simple Shapes
, edited by J. J.
Bowman
, T. B. A.
Senior
, and P. L. E.
Uslenghi
(North-Holland
, Amsterdam, The Netherlands
, 1969
), Chap. 10, pp. 353
–415
.16.
E. G.
Williams
, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
, 1st ed. (Academic
, London
, 1999
), p. 306
.17.
J.
Meyer
and G. W.
Elko
, “Position independent close-talking microphone
,” Signal Process.
86
, 1254
–1259
(2006
).18.
B.
Rafaely
, “Analysis and design of spherical microphone arrays
,” IEEE Trans. Speech Audio Process.
13
, 135
–143
(2005
).19.
R. O.
Duda
and W. L.
Martens
, “Range dependence of the response of a spherical head model
,” J. Acoust. Soc. Am.
104
, 3048
–3058
(1998
).20.
Z.
Li
and R.
Duraiswami
, “Hemispherical microphone arrays for sound capture and beamforming
,” in Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics
(2005
), pp. 106
–109
.21.
The sign in the powers of β is different from that in Allen and Berkley’s conventional image method, due to the change in the definition of Rp.
22.
Z.
Chen
and R. C.
Maher
, “Addressing the discrepancy between measured and modeled impulse responses for small rooms
,” in Proceedings of the Audio Engineering Society Conventions
(2007
), pp. 1
–14
.23.
Very low frequencies are omitted due to the fact that the spherical Hankel function hl(x) has a singularity around x = 0.
24.
J.
Meyer
and T.
Agnello
, “Spherical microphone array for spatial sound recording,”
in Proceedings of the Audio Engineering Society Conventions
, New York
(2003
), pp. 1
–9
.25.
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
, edited by M.
Abramowitz
and I. A.
Stegun
(Dover Publications
, New York
, 1972
), p. 1046
.26.
27.
D. P.
Jarrett
, E. A. P.
Habets
, M. R. P.
Thomas
, N. D.
Gaubitch
, and P. A.
Naylor
, “Dereverberation performance of rigid and open spherical microphone arrays: Theory & simulation
,” in Proceedings of the Joint Workshop on Hands-Free Speech Communication and Microphone Arrays (HSCMA)
, Edinburgh
, UK
(2011
), pp. 145
–150
.28.
D. B.
Ward
, “On the performance of acoustic crosstalk cancellation in a reverberant environment
,” J. Acoust. Soc. Am.
110
, 1195
–1198
(2001
).29.
B. D.
Radlović
, R.
Williamson
, and R.
Kennedy
, “Equalization in an acoustic reverberant environment: Robustness results
,” IEEE Trans. Speech Audio Process.
8
, 311
–319
(2000
).30.
T. T.
Sandel
, D. C.
Teas
, W. E.
Feddersen
, and L. A.
Jeffress
, “Localization of sound from single and paired sources
,” J. Acoust. Soc. Am.
27
, 842
–852
(1955
).31.
A.
Avni
and B.
Rafaely
, “Sound localization in a sound field represented by spherical harmonics
,” in Proceedings of the Second International Symposium on Ambisonics and Spherical Acoustics
, Paris, France
(2010
), pp. 1
–5
.32.
M. J.
Evans
, J. A. S.
Angus
, and A. I.
Tew
, “Analyzing head-related transfer function measurements using surface spherical harmonics
,” J. Acoust. Soc. Am.
104
, 2400
–2411
(1998
).33.
B. G.
Shinn-Cunningham
, N.
Kopco
, and T. J.
Martin
, “Localizing nearby sound sources in a classroom: Binaural room impulse responses
,” J. Acoust. Soc. Am.
117
, 3100
–3115
(2005
).34.
Although the ray-tracing formula is frequency independent, it has been shown (Ref. 35) that ITDs actually exhibit some frequency dependence, and that because the ray-tracing concept applies to short wavelengths, this model yields only the high frequency time delay. Kuhn provides a more comprehensive discussion of this model and the frequency dependence of ITDs (Ref. 36). It should be noted the simulation results in Fig. 8 are in broad agreement with Kuhn’s measured results at 3.0 kHz.
35.
C.
Brown
and R.
Duda
, “A structural model for binaural sound synthesis
,” IEEE Trans. Speech Audio Process.
6
, 476
–488
(1998
).36.
G. F.
Kuhn
, “Model for the interaural time differences in the azimuthal plane
,” J. Acoust. Soc. Am.
62
, 157
–167
(1977
).37.
J. R.
Deller
, J. G.
Proakis
, and J. H. L.
Hansen
, Discrete-Time Processing of Speech Signals
(MacMillan
, New York
, 1993
), p. 928
.© 2012 Acoustical Society of America.
2012
Acoustical Society of America
You do not currently have access to this content.