*Spatial Principal Component Analysis of Head-Related Transfer Functions and Its Domain… DOI: http://dx.doi.org/10.5772/intechopen.104449*

1990s [7]. On the other hand, the primitive form of the VADs was proposed in 1960s [1] and Morimoto *et al.* applied the theory into practice in 1980 [8]. Some of the VADs are known to be based on the synthesis of transfer functions involving the Head-Related Transfer Functions (HRTFs). They require the real-time processing on their variation due to the movement of the listener and/or the sound sources. Takane *et al.* proposed a theory of VAD named ADVISE (Auditory Display based on VIrtual SpherE model) [9], and reported an elemental implementation of the VAD based on ADVISE [10]. The listener's own HRTFs in all directions are ideally essential in order to carry out the synthesis. Moreover, various implementations of VADs exist based on the synthesis of binaural sound signals using the HRTFs, [7, 11–13]. Taking into account a set of HRTFs acquired for an individual in all directions, its data size must be as compact as possible with their synthesis accuracy achieved to some extent.

A possible approach to the compact representation for spatial variation of an individual HRTF is modeling. Haneda *et al.* proposed the Common Acoustical-Pole and Zero (CAPZ) model [14]. In the CAPZ model, it is assumed that the poles in HRTFs are independent of sound source positions while their zeros are dependent on them. They indicated that the spatial variation of the HRTFs of a dummy head was modeled in acceptable accuracy. Based on this model, Watanabe *et al.* proposed the interpolation method and this method showed good interpolation accuracy [15]. The CAPZ model is useful for the compact representation of the HRTFs since the sourceposition-independent poles makes the total number of coefficients for the representation of the HRTFs with their spatial variation. The data amount decreased by using the CAPZ model, however, is up to 50% relative to the case that all HRTFs in all directions are represented by the FIR filters with fixed length.
