Towards optimal functional representation of head-related transfer functions in the horizontal plane

Head-related transfer function (HRTF) individualization using principle component analysis (PCA) modelling rely on the empirical data to reduce HRTF dimensionality for an optimal representation and to achieve HRTF personalization by tuning the model weights with the subject anthropometric parameters. However, for these representations, the basis is discrete and data dependent which can limit its usefulness in universal HRTF representation. This paper studies the optimal functional representation of magnitude HRTF of 45 subjects for sound sources in the horizontal plane. We firstly use circular harmonics to extract the subject-independent HRTF angular dependence. The remaining spectral components of 45 subjects are then modelled by PCA and two standard functions, i.e., Fourier series and Fourier Bessel series. The metric to evaluate the model efficiency is the expansion weights cumulative variance. We identify that individual magnitude HRTFs over 20 kHz range could be modelled adequately well by a linear combination of only 19 Fourier Bessel series; this is a near optimal representation in comparison with the statistical PCA model. Further analysis of the model weights with subjective anthropometric measurements will provide a promising method for HRTF individualization, especially considering the nature of data independent continuous basis functions employed in the proposed functional representation.