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

out an experiment to evaluated his proposed estimation method of HRIRs from the impulse responses obtained in ordinary room with reflection [30]. The results showed that the subjects did not detect significant difference between the stimuli synthesized from the estimated and the original HRIRs when the SDR between them was more than about 20 dB. Nishino *et al.* investigated the interpolation accuracy of HRTFs in the median plane, although they did not carry out the subjective evaluation. The least (best) accuracy of their interpolation method is 2 dB in average SD [31]. Considering these researches, the least numbers of PCs to achieve the average SDR more than 20 dB and the average SD less than 2 dB were checked from the results of the SDR and SD computation. The results are shown in **Table 3**. It is found out from **Table 3** that number of PCs satisfying each condition has contrastive feature. The domains I, C and F have relatively small numbers satisfying the condition of average SDR > 20 dB, meaning that these domain can reconstruct the HRIRs in relatively high accuracy with small numbers of PCs. On the contrary, The domains L and CL have relatively small numbers satisfying the condition of average SD < 2 dB, meaning that these domains can reconstruct the amplitude of HRTFs relatively high accuracy with small numbers of PCs. The domain C has the balanced property in both time and frequency domain accuracies.

It is known that the frequency-domain spectral features in the HRTFs are important for the sound localization especially in the median plane [1, 32]. Iida *et al.* proposed a parametric model of the HRTF focused on the peaks and notches in the frequency domain, and showed that the first and second lowest notches (called N1 and N2, respectively) in their frequency spectra contribute to the subjects' perceived elevation [33]. These results may state that the local frequency domain features may cause the difference in the listener's perceived direction, and the reconstruction accuracy in frequency domain must be well taken into account to avoid such potential difference. These researches support the accuracy in frequency domain is more important than that in time domain. Based on such subjective properties together with the objective properties shown in this chapter, the domain L and CL are suitable for the SPCA of the HRTFs more than the other domains. On the other hand, the domains L and CL require relatively large number of PCs to achieve the CPV values when the CPV is closer to 1. The previous researches indicate that the reconstruction with relatively small number of PCs could make the HRTFs/HRIRs without audible difference [17, 19, 27, 28], therefore it is expected that the domains L and CL can bring about the acceptable subjective evaluation with small number of PCs. The difference in the domains for the SPCA must be investigated more in detail especially based on the subjective evaluation, which is one of the future studies concerning the contents of this chapter.


**Table 3.**

*The least number of components to achieve average SDR > 20 dB and average SD < 2 dB in each domain.*
