Multi-dimensional analysis of head-related transfer function based on tensor-SVD

Abstract

Recently, virtual multimedia such as 3D movie, broadcast, and virtual reality have been developed vividly with large demands and interests in many applications. Virtual Auditory Display (VAD), aims at generating spatialized virtual sound and conveying them to a listener. The Head-Related Transfer Function (HRTF), which is defined as an acoustic transfer function between sound pressure at a distal sound source and that measured in front of a listener’s ear drum, describes the physical transform of sound waves due to diffraction caused by the physical shape of a listener. HRTFs play a key role to render high-quality VAD. In this reason, various issues, e.g. interpretation, modeling, and customization of HRTFs, have been studied by many researchers. This thesis mainly focuses on interpretation of HRTFs using the multi-dimensional analysis method: Tensor Singular Value Decomposition (Tensor-SVD). The SVD can be used to obtain orthogonal basis functions and their weightings from each dimension. The major advantage of the Tensor-SVD among various SVD methods is that the dimension of multi-dimensional data can be efficiently reduced and can be analyzed independently. As a pre-processing, it is commonly accepted to subtract empirical mean of a dataset for the reduction of basis functions caused by the mean value in HRTF analysis. However, in case of the multi-dimensional data, the mean value can be extracted from various spaces, because the data tensor has more than two dimensions. The mean values having a vector, matrices, and a third-order tensor form are extracted. The effect of the several dimensions are prominently reduced, especially for azimuth and subject axes. Therefore, it is necessary to define and extract mean value from the appropriate dimension according to the purpose of the analysis. After extracting the proper mean value of the data, the multi-dimensional characteristics of HRTF in various domains are investigated: inter-aural time differences, time domain and log-magnitude (frequency) domain. The result shows that the analysis in particular domain has some merits and limitations. Therefore, in the multi-dimensional study of HRTF, selection of analyzing domain is necessary to utilize the characteristics of the domain. Also, the physical meanings of obtained basis functions and their weightings are explained in detail.