The equivalence between principal components analysis of head-related transfer functions in the time domain and frequency domain

PCA (principal components analysis) is a common way to analyze and reduce HRTFs (head-related transfer functions) data. Both PCA of HRTFs in the frequency domain and PCA of HRIRs (head-related impulse responses) in the time domain are frequently used. This paper proves that PCA of HRIRs in the time domain and PCA of HRTFs in the frequency domain are mathematically equivalent. Therefore, it implies that the possibility is very rare to obtain any new results from PCA of HRIRs in the time domain which can not be obtained from PCA of HRTFs in the frequency domain, vice versa.