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Approximating the head-related transfer function using simple geometric models of the head and torso.

The head-related transfer function (HRTF) for distant sources is a complicated function of azimuth, elevation and frequency. This paper presents simple geometric models of the head and torso that provide insight into its low-frequency behavior, especially at low elevations. The head-and-torso models are obtained by adding both spherical and ellipsoidal models of the torso to a classical spherical-head model. Two different numerical techniques--multipole reexpansion and boundary element methods--are used to compute the HRTF of the models in both the frequency domain and the time domain. These computed HRTFs quantify the characteristics of elevation-dependent torso reflections for sources above the torso-shadow cone, and reveal the qualitatively different effects of torso shadow for sources within the torso-shadow cone. These effects include a torso bright spot that is prominent for the spherical torso, and significant attenuation of frequencies above 1 kHz in a range of elevations. Both torso reflections and torso shadow provide potentially significant elevation cues. Comparisons of the model HRTF with acoustic measurements in the horizontal, median, and frontal planes confirm the basic validity of the computational methods and establish that the geometric models provide good approximations of the HRTF for the KEMAR mannequin with its pinnae removed.