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.

Acoustic interaction between the right and left piriform fossae in generating spectral dips.

It is known that the right and left piriform fossae generate two deep dips on speech spectra and that acoustic interaction exists in generating the dips: if only one piriform fossa is modified, both the dips change in frequency and amplitude. In the present study, using a simple geometrical model and measured vocal tract shapes, the acoustic interaction was examined by the finite-difference time-domain method. As a result, one of the two dips was lower in frequency than the two independent dips that appeared when either of the piriform fossae was occluded, and the other dip was higher in frequency than the two dips. At the lower dip frequency, the piriform fossae resonated almost in opposite phase, while at the higher dip frequency, they resonated almost in phase. These facts indicate that the piriform fossae and the lower part of the pharynx can be modeled as a coupled two-oscillator system whose two normal vibration modes generate the two spectral dips. When the piriform fossae were identical, only the higher dip appeared. This is because the lower mode is not acoustically coupled to the main vocal tract enough to generate an absorption dip.

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.

Visualisation of hypopharyngeal cavities and vocal-tract acoustic modelling.

The hypopharyngeal cavities consist of the laryngeal cavity and bilateral piriform fossa, constituting the bottom part of the vocal tract near the larynx. Visualisation of these cavities with magnetic resonance imaging (MRI) techniques reveals that during speech, the laryngeal cavity takes the form of a long-neck flask and the piriform fossa takes the form of a goblet of varying shapes: the former diminishes greatly in whispering and the latter disappears during deep inhalation. These cavities have been shown to exert significant acoustic effects at higher frequency spectra. In this study, acoustic experiments were conducted for male and female mechanical vocal tracts with the results that acoustic effects of those cavities determine the frequency spectra above 2 kHz, giving rise to peaks and zeros. An acoustic model of vowel production was proposed with three components: voice source, hypopharyngeal cavities and vocal tract proper, which provides effective means in controlling voice quality and expressing individual vocal characteristics.

Acoustic analysis of the vocal tract during vowel production by finite-difference time-domain method.

The vocal tract shape is three-dimensionally complex. For accurate acoustic analysis, a finite-difference time-domain method was introduced in the present study. By this method, transfer functions of the vocal tract for the five Japanese vowels were calculated from three-dimensionally reconstructed magnetic resonance imaging (MRI) data. The calculated transfer functions were compared with those obtained from acoustic measurements of vocal tract physical models precisely constructed from the same MRI data. Calculated transfer functions agreed well with measured ones up to 10 kHz. Acoustic effects of the piriform fossae, epiglottic valleculae, and inter-dental spaces were also examined. They caused spectral changes by generating dips. The amount of change was significant for the piriform fossae, while it was almost negligible for the other two. The piriform fossae and valleculae generated spectral dips for all the vowels. The dip frequencies of the piriform fossae were almost stable, while those of the valleculae varied among vowels. The inter-dental spaces generated very small spectral dips below 2.5 kHz for the high and middle vowels. In addition, transverse resonances within the oral cavity generated small spectral dips above 4 kHz for the low vowels.

Vocal tract length perturbation and its application to male-female vocal tract shape conversion.

An alternative and complete derivation of the vocal tract length sensitivity function, which is an equation for finding a change in formant frequency due to perturbation of the vocal tract length [Fant, Quarterly Progress and Status Rep. No. 4, Speech Transmission Laboratory, Kungliga Teknisha Hogskolan, Stockholm, 1975, pp. 1-14] is presented. It is based on the adiabatic invariance of the vocal tract as an acoustic resonator and on the radiation pressure on the wall and at the exit of the vocal tract. An algorithm for tuning the vocal tract shape to match the formant frequencies to target values, such as those of a recorded speech signal, which was proposed in Story [J. Acoust. Soc. Am. 119, 715-718 (2006)], is extended so that the vocal tract length can also be changed. Numerical simulation of this extended algorithm shows that it can successfully convert between the vocal tract shapes of a male and a female for each of five Japanese vowels.

Acoustic roles of the laryngeal cavity in vocal tract resonance.

The acoustic effects of the laryngeal cavity on the vocal tract resonance were investigated by using vocal tract area functions for the five Japanese vowels obtained from an adult male speaker. Transfer functions were examined with the laryngeal cavity eliminated from the whole vocal tract, volume velocity distribution patterns were calculated, and susceptance matching analysis was performed between the laryngeal cavity and the vocal tract excluding the laryngeal cavity (vocal tract proper). It was revealed that the laryngeal cavity generates one of the formants of the vocal tract, which is the fourth in the present study. At this formant, the resonance of the laryngeal cavity (the 1/4 wavelength resonance) induces the open-tube resonance of the vocal tract proper (the 3/2 wavelength resonance). At the other formants, on the other hand, the vocal tract proper acts as a closed tube, because the laryngeal cavity has only a small contribution to generating these formants and the effective closed end of the whole vocal tract is the junction between the laryngeal cavity and the vocal tract proper.

Cyclicity of laryngeal cavity resonance due to vocal fold vibration.

Acoustic effects of the time-varying glottal area due to vocal fold vibration on the laryngeal cavity resonance were investigated based on vocal tract area functions and acoustic analysis. The laryngeal cavity consists of the vestibular and ventricular parts of the larynx, and gives rise to a regional acoustic resonance within the vocal tract, with this resonance imparting an extra formant to the vocal tract resonance pattern. Vocal tract transfer functions of the five Japanese vowels uttered by three male subjects were calculated under open- and closed-glottis conditions. The results revealed that the resonance appears at the frequency region from 3.0 to 3.7 kHz when the glottis is closed and disappears when it is open. Real spectra estimated from open- and closed-glottis periods of vowel sounds also showed the on-off pattern of the resonance within a pitch period. Furthermore, a time-domain acoustic analysis of vowels indicated that the resonance component could be observed as a pitch-synchronized rise-and-fall pattern of the bandpass amplitude. The cyclic nature of the resonance can be explained as the laryngeal cavity acting as a closed tube that generates the resonance during a closed-glottis period, but damps the resonance off during an open-glottis period.