Experimental guided spherical harmonics based head-related transfer function modeling

Abstract

In this thesis we investigate the experimental guided spherical harmonics based Head-Related Transfer Function (HRTF) modeling where HRTFs are parameterized as frequency and source location. We focus on efficiently representing the HRTF variations in sufficient detail by mathematical modeling and the experimental measurements. The goal of this work is towards an optimal functional HRTF modeling taking into account the demands of decreasing the computational cost and alleviating the HRTF interpolation and/or extrapolation in the headphone based binaural systems. To represent HRTF by models, we firstly consider the high variability of HRTFs among individuals caused by the differentiation of the scattering effects of the individual bodies on the sound waves. We conduct a series of statistical analyses on an experimental HRTF database of human subjects to reveal the correlation between the physical features of human beings, especially pinna, head, and torso, and the corresponding HRTFs. The strategy enables us to identify a minimal set of physical features which strongly influence the HRTFs in a direct physical way. We next consider the continuity of the HRTF representation in both spatial and frequency domain. We define a functional HRTF model class in which the HRTF spatial representation has been justified to be well approximated by a finite number of spherical harmonics while HRTF frequency representation remains the focus of this thesis. In order to seek an efficient representation for HRTF frequency portion, we derive a metric that is able to numerically evaluate the efficiency of different complete orthonormal bases. We show that the complex exponentials form the most efficient basis. Given the identified basis, we then provide a solution to determine the dimensionality of the representation. To represent HRTF by measurements, we firstly consider the required angular resolution and the most suitable sampling scheme taking into account the two dimensional angular direction and the wide audio frequency range. We review the spherical harmonic analysis of the HRTF from which the least required number of spatial samples for HRTF measurement is derived. Considering how the HRTF data should be sampled on the sphere, we propose a list of requirements for the determination of the HRTF measurement grid. In addition to explaining how to measure the HRTF over sphere according to the identified scheme, we propose a fast spherical harmonic transform algorithm. We next consider the feasible experimental setup for a non-anechoic situation, that is, the measurements can be made when there is some reverberation. We emphasize on the design of the test signal and the post-processing to extract HRTFs.