A technique based on the virtual source representation is presented for modeling head-related transfer functions (HRTFs). This method is motivated by the theory of simple layer potential and the principle of wave superposition. Using the virtual source representation, the HRTFs for a human head with pinnae are calculated with a minimal amount of computation. In the process, a special regularization scheme is required to calculate the equivalent strengths of virtual sources. To justify the proposed method, tests were carried out to compare the virtual source method with the boundary element method (BEM) and a direct HRTF measurement. The HRTFs obtained using the virtual source method agrees reasonably well in terms of frequency response, directional response, and impulse response with the other methods. From the numerical perspectives, the virtual source method obviates the singularity problem as commonly encountered in the BEM, and is less computationally demanding than the BEM in terms of computational time and memory storage. Subjective experiments are also conducted using the calculated and the measured HRTFs. The results reveal that the spatial characteristics of sound localization are satisfactorily reproduced as a human listener would naturally perceive by using the virtual source HRTFs.

1.
Gardner
,
B.
, and
Martin
,
K.
, 1995, “
HRTF Measurements of a KEMAR
,”
J. Acoust. Soc. Am.
0001-4966,
97
, pp.
3907
3908
, http://sound.media.mit.edu/KEMAR.htmlhttp://sound.media.mit.edu/KEMAR.html
2.
Algazi
,
V. R.
,
Duda
,
R. O.
,
Thompson
,
D. M.
, and
Avendano
,
C.
, 2001, “
The CIPIC HRTF Database
,”
Proceedings of the 2001 IEEE Workshop on Applications of Signal Processing to Audio and Electroacoustics
,
Mohonk Mountain House
,
New Paltz, NY
, pp.
99
102
.
3.
Batteau
,
D. W.
, 1967, “
The Role of the Pinna in Human Localization
,”
Proc. R. Soc. London
0962-8452,
B168
, pp.
158
180
.
4.
Batteau
,
D. W.
, 1968,
Listening With the Naked Ear: The Neuropsychology of Spatially Oriented Behavior
,
Dorsey Press
, Homewood, IL.
5.
Brown
,
C. P.
, and
Duda
,
R. O.
, 1998, “
A Structural Model for Binaural Sound Synthesis
,”
IEEE Trans. Speech Audio Process.
1063-6676,
6
, pp.
476
488
.
6.
Algazi
,
V. R.
,
Duda
,
R. O.
,
Duraiswami
,
R.
,
Gumerov
,
N. A.
, and
Tang
,
Z.
, 2002, “
Approximating the Head-Related Transfer Function Using Simple Geometric Models of the Head and Torso
,”
J. Acoust. Soc. Am.
0001-4966,
112
, pp.
2053
2064
.
7.
Duda
,
R. O.
, 2000, “
3-D Audio for HCI
,” Report of Spatial Audio Project, Department of Electrical Engineering, San Jose State University, http://www.engr.sjsu.edu/~knapp/HCIROD3D/3D_home.htmhttp://www.engr.sjsu.edu/~knapp/HCIROD3D/3D_home.htm
8.
Kahana
,
Y.
, 2000, “
Numerical Modeling of the Head-Related Transfer Function
,” Ph.D. thesis, University of Southampton, Institute of Sound and Vibration Research.
9.
Nelson
,
P. A.
, and
Kahana
,
Y.
, 2001, “
Spherical Harmonics, Singular-Value Decomposition and the Head-Related Transfer Function
,”
J. Sound Vib.
0022-460X,
23
(
9
), pp.
607
637
.
10.
Walsh
,
T.
,
Demkowicz
,
L.
, and
Charles
,
R.
, 2004, “
Boundary Element Modeling of External Human Auditory System
,”
J. Acoust. Soc. Am.
0001-4966,
115
, pp.
1033
1043
.
11.
Koopmann
,
G. H.
,
Song
,
L.
, and
Fahnline
,
J. B.
, 1989, “
A Method for Computing Acoustic Fields Based on the Principle of Wave Superposition
,”
J. Acoust. Soc. Am.
0001-4966,
86
, pp.
2433
2438
.
12.
Song
,
L.
,
Koopmann
,
G. H.
, and
Fahnline
,
J. B.
, 1991, “
Numerical Errors Associated With the Method of Superposition for Computing Acoustic Fields
,”
J. Acoust. Soc. Am.
0001-4966,
89
, pp.
2626
2633
.
13.
Jeans
,
R.
, and
Mathews
,
I. C.
, 1992, “
The Wave Superposition Method as a Robust Technique for Computing Acoustic Fields
,”
J. Acoust. Soc. Am.
0001-4966,
92
, pp.
1156
1166
.
14.
Williams
,
E. G.
, 1999,
Fourier Acoustics
,
Academic Press
, NY.
15.
Schuhmacher
,
A.
,
Hald
,
J.
,
Rasmussen
,
K. B.
, and
Hansen
,
P. C.
, 2003, “
Sound Source Reconstruction Using Inverse Boundary Element Calculations
,”
J. Acoust. Soc. Am.
0001-4966,
113
, pp.
114
127
.
16.
SYSNOISE 5.6—Release Notes and Getting Started Manual, LMS International, Leuven, Belgium.
17.
SYSNOISE 5.6—User Manual, LMS International, Leuven, Belgium.
18.
D’Appolito
,
J.
, 1998,
Testing Loudspeakers
,
Audio Amateur Press
.
19.
MATLAB 6.5—Help Content, Mathworks, Inc.
20.
Oppenheim
,
A. V.
,
Schafer
,
R. W.
, and
Buck
,
J. R.
, 1999,
Discrete-Time Signal Processing
,
Prentice-Hall
, Englewood Cliffs, NJ.
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