Further observations on a principal components analysis of head-related transfer functions.

Humans can externalise and localise sound-sources in three-dimensional (3D) space because approaching sound waves interact with the head and external ears, adding auditory cues by (de-)emphasising the level in different frequency bands depending on the direction of arrival. While virtual audio systems reproduce these acoustic filtering effects with signal processing, huge memory-storage capacity would be needed to cater for many listeners because the filters are as unique as the shape of each person's head and ears. Here we use a combination of physiological imaging and acoustic simulation methods to confirm and extend previous studies that represented these filters by a linear combination of a small number of eigenmodes. Based on previous psychoacoustic results we infer that more than 10, and as many as 24, eigenmodes would be needed in a virtual audio system suitable for many listeners. Furthermore, the frequency profiles of the top five eigenmodes are robust across different populations and experimental methods, and the top three eigenmodes encode familiar 3D spatial contrasts: along the left-right, top-down, and a tilted front-back axis, respectively. These findings have implications for virtual 3D-audio systems, especially those requiring high energy-efficiency and low memory-usage such as on personal mobile devices.

Vertical normal modes of human ears: Individual variation and frequency estimation from pinna anthropometry.

Beyond the first peak of head-related transfer functions or pinna-related transfer functions (PRTFs) human pinnae are known to have two normal modes with "vertical" resonance patterns, involving two or three pressure anti-nodes in cavum, cymba, and fossa. However, little is known about individual variations in these modes, and there is no established model for estimating their center-frequencies from anthropometry. Here, with geometries of 38 pinnae measured, PRTFs were calculated and vertical modes visualized by numerical simulation. Most pinnae were found to have both Cavum-Fossa and Cavum-Cymba modes, with opposite-phase anti-nodes in cavum and either fossa or cymba, respectively. Nevertheless in both modes, fossa involvement varied substantially across pinnae, dependent on scaphoid fossa depth and cymba shallowness. Linear regression models were evaluated in mode frequency estimation, with 3322 measures derived from 31 pinna landmarks. The Cavum-Fossa normal mode frequency was best estimated [correlation coefficient r = 0.89, mean absolute error (MAE) = 257 Hz or 4.4%] by the distance from canal entrance to helix rim, and cymba horizontal depth. The Cavum-Cymba normal mode frequency was best estimated (r = 0.92, MAE = 247 Hz or 3.2%) by the sagittal-plane distance from concha floor to cymba anterior wall, and cavum horizontal depth.

Frequency and amplitude estimation of the first peak of head-related transfer functions from individual pinna anthropometry.

The first (lowest) peak of head-related transfer functions (HRTFs) is known to be a concha depth resonance and a spectral cue in human sound localization. However, there is still no established model to estimate its center-frequency F1 and amplitude A1 from pinna anthropometry. Here, with geometries of 38 pinnae measured and their median-plane HRTFs calculated by numerical simulation, linear regression models were evaluated in estimating F1 and A1 from 25 concha depth and aperture measurements. F1 was best estimated (correlation coefficient r = 0.84, mean absolute error MAE = 118 Hz) by lateral distances from the base of the posterior cavum concha to the outer surface of the antitragus and antihelix (longest measures of concha depth). A1 was best estimated (r = 0.83, MAE = 0.84 dB) by the lateral distance from the ear-canal entrance to the side of the cheek near the anterior notch (shortest measure of concha depth) and by the equivalent diameter of the concha aperture. These results suggest that the first resonance's quarter-wavelength corresponds to the longest lateral extent of the concha and that its energy lost to the surrounding air depends on the concha aperture and the cavum concha's shortest lateral depth.

Mechanism for generating peaks and notches of head-related transfer functions in the median plane.

It has been suggested that the first spectral peak and the first two spectral notches of head-related transfer functions (HRTFs) are cues for sound localization in the median plane. Therefore, to examine the mechanism for generating spectral peaks and notches, HRTFs were calculated from four head shapes using the finite-difference time-domain method. The comparison between HRTFs calculated from the whole head and the pinna-related transfer functions calculated from the segmented pinna indicated that the pinna determines the basic peak-notch pattern of the HRTFs. An analysis of the distribution patterns of pressure nodes and anti-nodes on the pinna computed in the steady state for sinusoidal excitations confirmed that the first three peaks correspond to the first three normal modes of the pinna. The analysis also revealed that at the first spectral notch frequencies, one or two anti-nodes appeared in the cymba and the triangular fossa, and a node developed in the concha. Furthermore, according to changes in the instantaneous pressure distribution patterns on the pinna, three types of mechanisms were hypothesized for inducing the node in the concha depending on the source elevation angle.