Conventional and spatial principal component analysis on near-field head-related transfer functions

Abstract

Head-related transfer functions (HRTFs) vary with both frequency and source position. The near-field HRTFs with source distance less than 1.0 m are particularly complicated due to their distance dependence. Principal component analysis (PCA), which is conventionally carried out in the frequency or time domain, has been widely applied to reduce the dimensionality of far-field HRTF data with source distance greater than 1.0 m. The present work firstly extends the conventional PCA, and then proposes a spatial PCA method in the spatial domain rather than in the frequency or time domain to reduce the dimensionality of near-field HRTF data. An illustrative case indicates that near-field HRTF magnitudes at 9 distances with 493 directions for each distance can be approximately represented by the weighted sum of 15 spectral shape basis functions using the conventional PCA or the weighted sum of 15 spatial basis functions using the spatial PCA. Both representations account for more than 98 % energy variation of the original data, and reduce the dimensionality of the original data to about a quarter. The proposed method is also applicable to the head-related impulse responses in the time domain. Furthermore, the spatial PCA scheme is potentially applicable to simplify near-field HRTF measurement. © 2013 Acoustical Society of America.