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TECHNICAL PAPERS

Numerical Modeling of Head-Related Transfer Functions Using the Boundary Source Representation

[+] Author and Article Information
Mingsian R. Bai1

Department of Mechanical Engineering, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsin-Chu 300 Taiwan, Republic of Chinamsbai@mail.nctu.edu.tw

Teng-Chieh Tsao

Department of Mechanical Engineering, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsin-Chu 300 Taiwan, Republic of China

1

Author to whom correspondence should be addressed.

J. Vib. Acoust 128(5), 594-603 (Apr 04, 2006) (10 pages) doi:10.1115/1.2203337 History: Received March 04, 2005; Revised April 04, 2006

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.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A generic L-curve. The solution norm is plotted versus the error norm with varying regularization parameter in the log-log scale.

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Figure 2

The photo of experimental arrangement for the HRTF measurement

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Figure 3

The mesh of the KEMAR dummy head for the IBEM: (a) head mesh; (b) pinna mesh. The vibrating source in the ear is indicated.

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Figure 4

The distribution of the surface nodes and virtual sources of the KEMAR: (a) side view; (b) front view

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Figure 5

L-curves of HRTF at 100Hz, obtained using the virtual source method. (a) The L-curve calculated using the original definition (the regularization parameter β multiplied by the first singular value is indicated on the curves); (b) the modified L-curve (the regularization parameter β is multiplied by the first singular value).

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Figure 6

HRTFs on the horizontal plane calculated using the IBEM: (a) Azimuth 0deg; (b) azimuth 90deg; (c) azimuth 270deg

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Figure 7

HRTFs calculated using the virtual source method on the horizontal plane: (a) azimuth 0deg; (b) azimuth 90deg; (c) azimuth 270deg

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Figure 8

The vertical polar coordinate system for the HRTF modeling

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Figure 9

The directional responses of HRTFs on the horizontal plane calculated using the IBEM. The magnitude is in linear scale and normalized with respect to the maximum. (a) HRTF at 500Hz; (b) HRTF at 2100Hz; (c) HRTF at 5100Hz; (d) HRTF at 9100Hz. (Dashed line: measured HRTF, solid line: calculated HRTF.)

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Figure 10

The directional responses of HRTFs on the horizontal plane calculated using the virtual source method. The magnitude is in linear scale and normalized with respect to the maximum. (a) HRTF at 500Hz; (b) HRTF at 2100Hz; (c) HRTF at 5100Hz; (d) HRTF at 9100Hz. (Dashed line: measured HRTF, solid line: calculated HRTF.)

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Figure 11

Head-related impulse response on the horizontal plane obtained from the HRTF calculated using the IBEM

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Figure 12

Head-related impulse response on the horizontal plane obtained from the HRTF calculated using the virtual source method

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Figure 13

Subjective experiment of azimuth localization using white noise input: (a) Measured HRTFs; (b) HRTFs calculated using the virtual source method; (c) HRTFs calculated using the IBEM

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Figure 14

Subjective experiment of elevation localization using white noise input: (a) Measured HRTFs; (b) HRTFs calculated using the virtual source method; (c) HRTFs calculated using the IBEM

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