**3. Relation between number of PCs and accuracy**

## **3.1 Conditions of analysis**

A database of HRIRs of KEMAR HATS (Head And Torso Simulator) provided by Media lab. of MIT [26] was used. Liang *et al.* used the same data in their study with the similar purpose to the one in this chapter. While they used the HRTFs only in horizontal plane [23], all data in this database involving 710 pairs of HRIRs (total: 1420) with sampling frequency of 44.1 kHz were used for the investigation in this chapter. Number of HRIRs is 1420, corresponding to *M* in Eqs. (4) and (5).

The initial delay in each response was extracted, then 256 sample points were taken as the data for the analysis, windowing with latter half of 512-points Blackman-Harris window function adjusting its peak at that of the HRIR. The SPCA was executed by constructing the covariance matrices from the HRIRs (called as domain I), the HRTFs (domain C), the amplitude of HRTFs (domain F), the log-amplitude of HRTFs (domain L), and the complex logarithm of HRTFs (domain CL). The HRTFs/HRIRs in all directions (710 directions�2 ears) were used, and the average vector (Eq. (4)) and the covariance matrix (Eq. (5)) were calculated in each case.
