Efficient Representation of Head-Related Transfer Functions With Combination of Spherical Harmonics and Spherical Wavelets

Recently, a modeling method for head-related transfer functions (HRTFs) in the spatial domain is proposed based on spherical wavelets. Because spherical wavelets are local functions on the sphere, HRTF local features can be efficiently represented by using a small number of analysis functions. This sparse representation method enables to control the spatial resolutions of a desired local region on the sphere with the expansion coefficients. Meanwhile, the conventional HRTF spatial variations models based on spherical harmonic decomposition, which is able to represent the HRTF coarse structure well with lower order models. In this paper, a modeling method of the HRTF spatial features is proposed by combining the spherical harmonics and spherical wavelets, which represents the coarse structure and spatial detail of the HRTFs, respectively. The numerical experiment results show that the proposed joint modeling method has smaller approximation errors within the frequency range of 7 kHz compared with 15 orders spherical harmonics modeling when the same number of parameters is used for representing the HRTF magnitude in all directions. In the comparisons with higher orders spherical harmonics modeling, the proposed joint modeling method yields smaller approximation errors within the frequency range of 20 kHz. Furthermore, the proposed joint modeling method is expected to help interpret the spatial cues in which the low orders spherical harmonic coefficients corresponds to head shadow effects while the spherical wavelet coefficients corresponding to the residual finer details may be interpreted as pinna effects. A tool for the HRTF spatial feature extraction is provided in this paper.