*3.3.1 Changes of SDR and SD with source direction*

Examples of the changes of the SDR with the source direction are plotted in **Figures 3**–**6**. **Figures 3**–**6** are figures for the SDR and the SD, respectively. For the elevation, elevation angles of 0°, 90° and 90° respectively correspond to the horizontal plane, above and below the subject. The lines were plotted in these figures with 20° interval from 40° to 80°, namely the 6 lines are in each figure. For the azimuth angles, their arrangements are the same as the original data [26], *i. e.*, 0°, 90°, 180° and 270° respectively correspond to the front, right, back, and left of the subject. In each figure, number of components in each domain was set to the least value satisfying two of the CPVs in **Table 2**. The first value is 0.95 in **Figures 3** and **5**, and the second is 0.999 in **Figures 4** and **6**.

#### **Figure 3.**

*Change of SDR in source azimuth at various elevation in each cases with number of PCs set to the least value achieving the cumulative proportion of variance of 0.95 in Table 2. (a) Domain I (No. of PCs = 10). (b) Domain C (No. of PCs = 6). (c) Domain F (No. of PCs = 7). (d) Domain L (No. of PCs = 11). (e) Domain CL (No. of PCs = 4).*

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

#### **Figure 4.**

*Change of SDR in source azimuth at various elevation in each cases with number of PCs set to the least value achieving the cumulative proportion of variance of 0.999 in Table 2. (a) Domain I (No. of PCs = 39). (b) Domain C (No. of PCs = 20). (c) Domain F (No. of PCs = 31). (d) Domain L (No. of PCs = 78). (e) Domain CL (No. of PCs = 39).*

Seeing these figures, macroscopic tendency in the change of the SDR and SD with the number of PCs is similar: the larger CPV value brings about the larger SDR and smaller SD, and these values are roughly the same when the CPV values is set equal among five domains. In contrast, it should be emphasized that the values of SD for the domains L and CL are smaller than those in the other domains, as shown in **Figure 5 (d), (e)** and **6(d), (e)**. The domains using the real and complex logarithm may give relatively smaller distortions in frequency domain.

Seeing the properties in time domain according to **Figures 3** and **4**, the values of SDR are gradually higher when the CPV value is larger. When the azimuth corresponds to the contralateral side (around 250° 300°) and especially at the lower elevation angles (less than 0°), the relatively smaller SDR values are found out also commonly in all domains In

#### **Figure 5.**

*Change of SD in source azimuth at various elevation in each cases with number of PCs set to the least value achieving the cumulative proportion of variance of 0.95 in Table 2. (a) Domain I (No. of PCs = 10). b) Domain C (No. of PCs = 6). (c) Domain F (No. of PCs = 7). (d) Domain L (No. of PCs = 11). (e) Domain CL (No. of PCs = 4).*

these azimuths and elevation angles, the relatively larger SD values are also observed, as shown in **Figures 5** and **6**. Xie stated the same points in his articles [19, 22]. In those range of directions, the HRIRs are very small in their energy because of the subject's head making a "shadow" making the sound from the sound source hard to reach especially in the high frequency range [1]. As a result, the HRIRs in those directions are relatively difficult to be reconstructed with a small number of PCs.
