^{1,a)}, Parham Mokhtari

^{1}, Hiroaki Kato

^{1}, Ryouichi Nishimura

^{1}and Kazuhiro Iida

^{2}

### Abstract

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.

I. INTRODUCTION

II. MATERIALS AND METHODS

A. MRI data

B. Calculation of HRTFs and pinna-related transfer functions (PRTFs)

C. Calculation of distribution patterns of pressure nodes and anti-nodes on the pinna

III. RESULTS AND DISCUSSION

A. Comparison between HRTFs and PRTFs

B. Peak–notch patterns on PRTFs

C. Distribution patterns of pressure nodes and anti-nodes at P1–P3

D. Distribution patterns of pressure nodes and anti-nodes at N1

E. Hypothesis of mechanism for inducing a node in the concha

IV. CONCLUSION

### Key Topics

- Normal modes
- 11.0
- Finite difference time domain calculations
- 9.0
- Magnetic resonance imaging
- 8.0
- Acoustic pattern recognition
- 5.0
- Acoustic analysis
- 4.0

## Figures

A schematized peak–notch pattern of HRTFs in the median plane, based on Figs. 1 and 8 in Raykar *et al.* (2005). Note that this figure is rotated 90° from its original presentation, and thus the horizontal axis indicates frequency and the vertical axis indicates elevation angle.

A schematized peak–notch pattern of HRTFs in the median plane, based on Figs. 1 and 8 in Raykar *et al.* (2005). Note that this figure is rotated 90° from its original presentation, and thus the horizontal axis indicates frequency and the vertical axis indicates elevation angle.

Anatomical nomenclature of the pinna. a: Scaphoid fossa. b: Triangular fossa. c: Cymba conchae (cymba). d: Cavity of concha (concha). e:Ear canal. f: Crus of helix. g: Antihelix. h: Tragus.

Anatomical nomenclature of the pinna. a: Scaphoid fossa. b: Triangular fossa. c: Cymba conchae (cymba). d: Cavity of concha (concha). e:Ear canal. f: Crus of helix. g: Antihelix. h: Tragus.

Whole heads of four subjects (upper panel) and the left pinnae segmented from the heads (lower panel). The black circles pointed out with black arrows in the lower panel indicate the source point for calculation of PRTFs and HRTFs.

Whole heads of four subjects (upper panel) and the left pinnae segmented from the heads (lower panel). The black circles pointed out with black arrows in the lower panel indicate the source point for calculation of PRTFs and HRTFs.

(a) HRTFs were calculated at 1.0 m in the median plane. (b) PRTFs were calculated at 0.1 m in the sagittal plane passing through the source point denoted by the white circles in the lower panel of Fig. 3. (c) When PRTFs were calculated, the source point was placed just outside of the blocked meatus and a total of 36 observation points were placed on the circumference of a circle with 0.1 m radius. A Gaussian pulse was input to the source point and pressure changes for all the observation points were obtained in a single computational run. (d) In contrast, when the pressure distribution pattern on the pinna was calculated, the source point was placed at the observation point used in the calculation of PRTFs.

(a) HRTFs were calculated at 1.0 m in the median plane. (b) PRTFs were calculated at 0.1 m in the sagittal plane passing through the source point denoted by the white circles in the lower panel of Fig. 3. (c) When PRTFs were calculated, the source point was placed just outside of the blocked meatus and a total of 36 observation points were placed on the circumference of a circle with 0.1 m radius. A Gaussian pulse was input to the source point and pressure changes for all the observation points were obtained in a single computational run. (d) In contrast, when the pressure distribution pattern on the pinna was calculated, the source point was placed at the observation point used in the calculation of PRTFs.

(a) Input volume velocity (Gaussian pulse) given by Eq. (1). (b) Calculated pressure changes at 0.1 m from the source point in free space. (c) Frequency characteristics of pressure changes of (b).

(a) Input volume velocity (Gaussian pulse) given by Eq. (1). (b) Calculated pressure changes at 0.1 m from the source point in free space. (c) Frequency characteristics of pressure changes of (b).

(Color online) HRTFs and PRTFs of four subjects. The scale bars indicate the log-power in dB.

(Color online) HRTFs and PRTFs of four subjects. The scale bars indicate the log-power in dB.

Peak patterns on PRTFs (left) and notch patterns on PRTFs (right). The scale bars indicate the log-power in dB. Note that the dark regions in panels (a), (c), (e), and (g) indicate higher log-power spectral amplitudes of PRTFs, while the dark regions in panels (b), (d), (f), and (h) indicate lower log-power spectral amplitude of PRTFs.

Peak patterns on PRTFs (left) and notch patterns on PRTFs (right). The scale bars indicate the log-power in dB. Note that the dark regions in panels (a), (c), (e), and (g) indicate higher log-power spectral amplitudes of PRTFs, while the dark regions in panels (b), (d), (f), and (h) indicate lower log-power spectral amplitude of PRTFs.

The upper panel shows PRTFs for M2 below 12 kHz to indicate the frequency and each elevation angle chosen for the lower panel. The scale bar indicates the log-power in dB. The lower panel indicates the distribution patterns of pressure nodes and anti-nodes at the first, second, and third normal modes of the pinna. Arrows represent the source direction.

The upper panel shows PRTFs for M2 below 12 kHz to indicate the frequency and each elevation angle chosen for the lower panel. The scale bar indicates the log-power in dB. The lower panel indicates the distribution patterns of pressure nodes and anti-nodes at the first, second, and third normal modes of the pinna. Arrows represent the source direction.

The upper panel shows PRTFs for M2 below 12 kHz to indicate the frequency and each elevation angle chosen for the lower panels. The scale bar indicates the log-power in dB. The lower panels indicate the three types of distribution patterns of pressure nodes and anti-nodes on the pinna (see the text). Arrows represent the source direction.

The upper panel shows PRTFs for M2 below 12 kHz to indicate the frequency and each elevation angle chosen for the lower panels. The scale bar indicates the log-power in dB. The lower panels indicate the three types of distribution patterns of pressure nodes and anti-nodes on the pinna (see the text). Arrows represent the source direction.

Notch patterns of PRTFs of all four subjects, indicating the three types of distribution patterns of pressure nodes and anti-nodes on the pinna (see the text) for each N1 trajectory. The scale bars indicate the log-power in dB.

Notch patterns of PRTFs of all four subjects, indicating the three types of distribution patterns of pressure nodes and anti-nodes on the pinna (see the text) for each N1 trajectory. The scale bars indicate the log-power in dB.

The mechanisms by which the propagating waves induce a node in the concha for the three types of distribution patterns of pressure nodes and anti-nodes on the pinna of M2, as shown in Fig. 9.

The mechanisms by which the propagating waves induce a node in the concha for the three types of distribution patterns of pressure nodes and anti-nodes on the pinna of M2, as shown in Fig. 9.

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