Numerical modelling of the head-related transfer function

Abstract

This thesis investigates various aspects of numerically modelled individualised HRTFs. The computer simulations (undertaken on both a parallel computer and a PC) are based on the exact solution of the wave equation, with the main emphasis on the Boundary Element Method (BEM). The basic features of the HRTF are investigated first with simple geometrical models such as a sphere and an ellipsoid that represent the human head, and a baffled cylinder that represents the concha. Accurate geometric models of two heads and six pinnae are captured by using state-of-the-art 3-D laser scanners and digitisers. These computer models are converted to valid BEM models and their frequency response is simulated. With current hardware technology, and vigilant optimisation of the manipulated mesh models and the solving procedures, baffled pinnae can be investigated up to 20 kHz, and heads with pinnae (but without torso) can be investigated up to 10-15 kHz. High accuracy is obtained when the results of the simulation at the blocked ear canal are compared with measurements made with especially designed and built apparatus in an anechoic chamber, using the same physical head and pinnae used in the simulations.

Once the results of the simulations are validated against measurements, further acoustic features of the external ear are investigated with an emphasis on the 'mode shapes' of the human pinna. Using the Singular Value Decomposition (SVD), the matrix of Green functions relating the acoustic pressure at 'field' points and 'source' points in space is analysed at discrete frequencies. When the field point and the source points are positioned on uniformly sampled spheres, a connection is found between the matrices of the singular vectors and the sampled spherical harmonics. When the method is investigated numerically, and the 'field' points are positioned on different pinnae, their 'mode shapes' are presented, and compared to the classical experiments made by E.A.G. Shaw in the 1970s. The method is investigated further in order to produce 'reduced order' transfer functions by taking into account only the most dominant features of the singular vectors.

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