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Deepening of PRTF notches by selective modification ofpinna surface reflection coefficient*○ Parham MOKHTARI，Yutaro HIROTA，Daisuke MORIKAWA（Toyama Prefectural University）
1

Introduction

2

Auditory cues for human sound localization in
the vertical dimension (e.g., elevation angle in themedian plane) are primarily the first two peaks
and notches of head-related transfer functions(HRTFs) [1]. As these cues are generated byacoustic reflections within the outer-ear (pinna)cavities, they are essentially the same as thepeaks and notches of pinna-related transferfunctions (PRTFs). In the median plane, typicallythe peak frequencies are invariant while thenotches vary with elevation angle [2].
Previous research has shown that broadband
sounds delivered by headphones or tube-phones
can be correctly externalized in front, provided
the listener’s peaks and notches are not overly
smoothed [3], or a typical mean depth of the first
two notches is either maintained or deepened [4].
In our experience with measurement/simulationof a range of pinnae, notches are not always deepand clearly defined at all elevation angles. An
intriguing question then arises whether artificiallydeepening notches where they are not alreadyclearly defined, may help enhance a listener’s
sound localization or spatial hearing in general.
With this motivation, we are interested in how
the notches depend on pinna surface reflection orshape. Previously, we used acoustic simulation tocalculate shifts in the first notch’s frequency andamplitude in response to local (2 mm) changes in
pinna surface reflection coefficient[5]. Here,
we extend that work by varying
jointly at
multiple pinna-surface elements chosen carefully
based on a prior sensitivity analysis, andobserving the effect on the notch depth. Our
research question is therefore whether, and towhat extent, a notch can be deepened by
judicious tuning of pinna surface reflection.
*Baseline Simulation

An MRI-measured & voxelated right ear’s [6]
PRTF at a front location 1 m from the head center
was calculated by 3D finite-difference time
domain (FDTD) simulation with grid resolution
2 mm. The Kirchhoff-Helmholtz method wasused to project the sound field around the pinnato the farfield observation point [7]. Sound speed
and medium density
at each voxel were set
to values for either air or water; the baselinereflection coefficient at the air-pinna interface
was thus= 0.999. The peaks and notches of
the calculated baseline PRTF (black curve inFig. 2) are listed in Table 1.
Table 1 Baseline PRTF peak (P) and notch (N)frequencies (F) and gain amplitudes (A)
P1
N1 N2
P2
N3P3F (Hz) 3860 7378 9116 10243 11054 13222
A (dB) +14.5 -22.2 -19.6 +2.1 -14.0 +11.43

Single-Voxel Perturbations

Keeping the same pinna shape,
andateach of the 1786 surface-voxels were modified
one voxel at a time such that
= 0.5 at onlythat part of the surface, and each time the PRTF
at 1 m in front was calculated. N1 frequency andamplitude were extracted on each PRTF and thebaseline values were subtracted to obtain ∆F and∆A. The 1786 pairs of deviations thus obtained
are shown as a scatterplot in Fig. 1(a). The pinna
sensitivity map for ∆A of N1 for the same data
was shown previously (Fig.2(a) in [5]).

4Multi-Voxel Perturbations

Next, a subset of surface voxels was selected,
with the aim of deepening N1 while minimizing
any effect on its frequency. Although there may
be many possible ways to make such a selection,
we simply defined a parabola ∆ =一部の耳介表面反射係数の選択的変更による PRTF ノッチの深化
モクタリ パーハム, 廣田 裕太郎, 森川 大輔 （富山県立大学）

日本音響学会講演論文集- 649 -

2022年3月

Fig. 1 (a) Effect of single-voxel perturbations on
N1 frequency and amplitude, and the 26 voxels
selected by a parabola (red); (b) a 3D view ofthe pinna highlighting the 26 selected voxels.
−0.0046(∆ ) − 1.4 on the scatterplot ofFig. 1(a), and chose all voxels that lay below thecurve. The 26 voxels thus selected on the basis of
their individual effects on N1, are colored on thepinna shown in Fig. 1(b).
Properties
andat these 26 voxels werethen jointly modified, such thatat only thoseparts of the pinna surface would be 0.5 as withthe single-voxel perturbations. However, theresulting PRTF (dashed curve in Figs. 2 & 3) hada much shallower N1 and N2. Therefore, we
modified the 26 voxels more subtly, such thatwould be gradually reduced in the following 8
steps: 0.97 , 0.95 , 0.94 , 0.93 , 0.92 , 0.91 ,0.89, and 0.87.
The resulting PRTFs up to 15 kHz are shownin Fig. 2, and Fig. 3 shows an expanded viewaround N1 & N2 separately. In Figs. 2 & 3, thebaseline PRTF is in black, the PRTFs for the 8
steps listed above are in various shades of blue,
and red highlights the PRTF at= 0.93, which
attained the deepest N1 & N2. As the 26 selectedvoxels’
was reduced from 0.999 to 0.93,
N1 and N2 sharpened and their amplitudes
monotonically decreased, N1 reaching −53.6 dB
and N2 reaching −61.7 dB. At the deepest levels,
N1 frequency shifted from the baseline by only
−70 Hz (i.e., by < 1 %), and N2 frequency
shifted by only +2 Hz; thus, as intended in thevoxel selection, notch frequencies were relativelyunaffected. Further reduction of
below 0.93
gradually broadened and shallowed the notches.
Meanwhile, the perturbations had almost no日本音響学会講演論文集

Fig. 2 Calculated PRTFs at 1 m in front.
Black: baseline condition. Various blue:atthe 26 selected voxels reduced in steps.
Red: deepest N1 and N2 at= 0.93.

Fig. 3 Same as Fig. 2, zoomed in on N1 & N2.
influence on the PRTF’s peaks and notches atother frequencies.

5Conclusions

A method was presented that, in principle, candeepen a PRTF’s first two notches. Future work
includes understanding the significance of theselected pinna-surface voxels in terms of thenotch generation mechanism, extending themethod to more than one farfield location, andinvestigating the auditory-perceptual effects ofsuch modifications.
Acknowledgements
This work was partially supported by JSPS
KAKENHI Grant Number JP17K00260.
References[1] Iida & Ishii, Appl. Acoust. 129, 239-247, 2018.
[2] Takemoto et al., JASA 132, 3832-3841, 2012.
[3] Kulkarni & Colburn, Nature, 747-749, 1998.
[4] Nishiyama & Iida, Proc.ASJ-Aut., 661-664, 2021.
[5] Hirota et al., Proc.ASJ-Aut., 651-652, 2021.
[6] Hirahara et al., Fundam. Review 2, 68-85, 2009.
[7] Mokhtari et al., Proc.ASJ-Aut., 611-614, 2008.

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