**Abstract**

In this chapter, the Principal Component Analysis (PCA) was adopted to spatial variation of Head-Related Transfer Function (HRTF) or its corresponding inverse Fourier Transform, called Head-Related Impulse Response (HRIR), in order to compactly represent their spatial variation. This is called the Spatial PCA (SPCA). The SPCA was carried out for a database of HRTFs in all directions by selecting the domain as one of the HRIRs, the complex HRTFs, the frequency amplitudes of HRTFs, log-amplitudes of HRTFs, and complex logarithm of HRTFs. The minimum phase approximation was incorporated for the frequency amplitudes and logamplitudes of HRTFs. Comparison of the accuracies in both time and frequency domains taking into account their influence on subjective evaluation showed that the log-amplitudes and complex logarithm of HRTFs are suitable for the SPCA of HRTFs.

**Keywords:** spatial principal component analysis, head-related transfer function, head-related impulse response, domain, compact representation
