Magnitude Modelling of HRTF Using Principal Component Analysis Appliedto Complex Values

Archives of Acoustics

2014

No 4

Oscar Alberto RAMOS, Fabian Carlos TOMMASINI

HRTF, PCA, binaural audition, auditory perception

Nauki Techniczne

Principal components analysis (PCA) is frequently used for modelling the magnitude of the head-
related transfer functions (HRTFs). Assuming that the HRTFs are minimum phase systems, the phase is
obtained from the Hilbert transform of the log-magnitude. In recent years, the PCA applied to HRTFs
is also used to model individual HRTFs relating the PCA weights with anthropometric measurements
of the head, torso and pinnae. The HRTF log-magnitude is the most used format of input data to the
PCA, but it has been shown that if the input data is HRTF linear magnitude, the cumulative variance
converges faster, and the mean square error (MSE) is smaller. This study demonstrates that PCA applied
directly on HRTF complex values is even better than the two formats mentioned above, that is, the MSE
is the smallest and the cumulative variance converges faster after the 8th principal component. Different
objective experiments around all the median plane put in evidence the differences which, although small,
seem to be perceptually detectable. To elucidate this point, psychoacoustic discrimination tests are done
between measured and reconstructed HRTFs from the three types of input data mentioned, in the median
plane between −45◦ and +90◦.

Committee on Acoustics PAS, PAS Institute of Fundamental Technological Research, Polish Acoustical Society

ISSN 0137-5075
;
eISSN 2300-262X