Comparison of Head-related Transfer Function Models Based on Principal Components Analysis

Abstract

This study deals with modeling of head-related transfer functions(HRTFs) using principal components analysis(PCA) in the time and frequency domains. Four PCA models based on head-related impulse responses(HRIRs), complex-valued HRTFs, augmented HRTFs, and log-magnitudes of HRTFs are investigated. The objective of this study is to compare modeling performances of the PCA models in the least-squares sense and to show the theoretical relationship between the PCA models. In terms of the number of principal components needed for modeling, the PCA model based on HRIR or augmented HRTFs showed more efficient modeling performance than the PCA model based on complex-valued HRTFs. The PCA model based on HRIRs in the time domain and that based on augmented HRTFs in the frequency domain are shown to be theoretically equivalent. Modeling performance of the PCA model based on log-magnitudes of HRTFs cannot be compared with that of other PCA models because the PCA model deals with log-scaled magnitude components only, whereas the other PCA models consider both magnitude and phase components in linear scale.