Content uploaded by Viktor Gunnarsson
Author content
All content in this area was uploaded by Viktor Gunnarsson on Aug 28, 2023
Content may be subject to copyright.
Audio Engineering Society
Conference Paper
Presented at the International Conference on
Spatial and Immersive Audio
2023 August 23–25, Huddersfield, UK
This paper was peer-reviewed as a complete manuscript for presentation at this conference. This paper is available in the AES
E-Library (http://www.aes.org/e-lib), all rights reserved. Reproduction of this paper, or any portion thereof, is not permitted
without direct permission from the Journal of the Audio Engineering Society.
Robust Binaural Measurements in the Ear Canal Using a
Two-Microphone Array
Viktor Gunnarsson1,2 and Sead Smailagi´
c2,3
1Signals and Systems Division, Uppsala University, Sweden
2Dirac Research AB, Uppsala, Sweden
3Signaton AB, Helsingborg, Sweden
Correspondence should be addressed to Viktor Gunnarsson (viktor.gunnarsson@dirac.com)
ABSTRACT
Accurate binaural rendering requires accurate reproduction of binaural signals at the eardrum, which in turn requires
adequate binaural technology. We propose a method to measure head-related & headphone transfer functions with
a two-microphone array in the ear canal. By implementing a cardioid directional pattern, the forward and reverse
propagating sound pressure components are measured separately, thus avoiding the influence of standing waves in
the ear canal on the measurements. The method is useful in filter design for individualized binaural rendering that,
compared with the blocked-canal method, does not assume acoustically ’open’ headphones to be used. The method
also mitigates the excessive sensitivity to microphone position of regular open-canal measurements. Validation
measurements are conducted using a natural scale replica ear and a MEMS microphone array.
1 Introduction
Headphone-based binaural rendering allows for realis-
tic reproduction of auditory experiences if the repro-
duced sound pressure at the eardrums matches that of a
real sound field or sound source in a certain direction
[
1
–
3
]. However, accurate reproduction of binaural sig-
nals at the eardrums is challenging and requires careful
attention to binaural measurement technique and filter
design [
4
]. In principle, an anechoic sound recording
can be rendered as a virtual source in direction
Ω
by
convolving it with a filter
Hv(ω,Ω)
, unique for each
ear, defined as
Hv(ω,Ω) = HRT F (ω,Ω)
H pT F (ω).(1)
where
ω
is angular frequency,
HRT F (ω,Ω)
is the
Head-Related Transfer-Function (HRTF) that describes
the sound transfer function from free-field to a well-
defined point in the ear, and
H pT F (ω)
is the head-
phone transfer function to the same point. Both HRTFs
and HpTFs vary greatly between individuals [
5
,
6
]. Cre-
ating a virtual auditory space with minimum timbral
artifacts, correct localization, and full externalization
thus generally requires both individual HRTFs [
5
], and
individual HpTFs [7, 8].
A fundamental consideration in binaural technology
is the selection of a reference point in the ear where
HRTFs and HpTFs are measured. The ear canal can be
likened to a tube that is open at one end and closed at
the other. Due to its small diameter, around 7.4 mm on
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
average, wave propagation within the ear canal is of-
ten modeled as one-dimensional at audible frequencies.
However, the length of the ear canal, around 25 mm on
average, is not negligible compared to the wavelength,
and a standing wave pattern exists in the ear canal that
makes measurements in the ear canal strongly depen-
dent on the exact measurement position. Therefore,
HRTFs and HpTFs that are to be combined as in Eq.
(1) need to refer to the same reference point.
Hammershøi et. al confirmed that sound transmission
to the eardrum from different points in the ear canal
is independent of the direction of incidence of sound
to the head [
9
]. They concluded this to be valid over
most of the audible spectrum, including from the open
or blocked ear canal entrance. An implication of this
is that any point in the ear canal can be selected as the
reference point when measuring HRTFs and HpTFs
while theoretically achieving accurate sound reproduc-
tion at the eardrum. Measurements in the ear canal can
for example be conducted using a miniature electret or
MEMS microphone. In practice, it is often challenging
to avoid a small occasional repositioning of the in-ear
microphone in between the HRTF and HpTF measure-
ments, for example when taking the headphones on or
off, or due to head movements. This leads to inevitable
coloration being introduced in the binaural rendering
filter of Eq. (1), which will be further elaborated on in
section 2.1 of this article.
One choice of reference point is to measure directly at
the eardrum, as in e.g. [
1
]. Probe tube microphones are
typically used to avoid damaging the delicate eardrum.
In addition to the possible discomfort of such mea-
surements, a complicating factor is that the eardrum
position is not defined by a single point along the canal
since it terminates the ear canal at an oblique angle. At
the highest audible frequencies, the exact probe posi-
tion at the eardrum has a large effect on the measured
response [10].
The most common reference point for HRTF measure-
ments is at the blocked ear canal entrance [
11
], for sev-
eral reasons. HRTF measurements at the blocked ear
canal are considered to retain full spatial information
[
12
]. Compared to measurements at the open ear canal,
the blocked-canal method removes a source of individ-
ual variation from HRTF or HpTF measurements that
is due to the individual ear canal acoustics, thus making
the measurements more suitable for non-individualized
reproduction [
9
,
12
]. It is also relatively easy to achieve
a stable and well-defined microphone position with the
blocked-canal method. However, accurate reproduc-
tion of sound pressure at the eardrum with the blocked-
canal method generally relies on the assumption that
the headphones used have free-air equivalent coupling
(FEC) to the ear, i.e., that the headphones are acousti-
cally ’open’ and do not significantly affect the acoustic
impedance seen from the ear canal. Otherwise, a col-
oration is introduced corresponding to the so-called
pressure-division ratio [
6
]. The FEC condition is some-
what limiting as most headphones on the market are
not fully FEC compatible.
The trade-offs involved with the above-mentioned
methods have incited further research into binaural
measurement methods. Hiipakka et. al. used a minia-
ture pressure-velocity sensor to measure sound pres-
sure and particle velocity at the entrance of the open
ear canal [
13
,
14
]. They proposed a method to esti-
mate the sound pressure at the eardrum based on the
acoustic energy density at the ear canal entrance. In
an evaluation of the method for individualized binau-
ral synthesis, it performed significantly better than the
blocked-canal method both with regards to the mea-
sured error in sound pressure at the eardrum [
13
], and
in a listening test on perceived coloration [
15
]. A fac-
tor preventing the adoption of this method, however,
is that miniature pressure-velocity sensors suitable for
binaural measurements are so far not widely available
in the marketplace.
In this article, we propose a two-microphone method
suitable for open-canal binaural measurements that can
be used with low-cost miniature MEMS microphones.
By implementing a cardioid pickup pattern using two
closely spaced microphones, the forward (incident) and
reverse (reflected) propagating sound waves in the ear
canal can be measured separately. Thus, by avoiding
the influence of standing-wave patterns on the mea-
surements, the exact microphone location in the ear
canal becomes much less critical compared to single-
microphone open ear canal measurements, and evalu-
ation of Eq. (1) becomes more robust to small micro-
phone displacements during the measurement session.
There is also no requirement for FEC-compatible head-
phones.
Section 2 presents the proposed method by first analyz-
ing simulations on a simple ear canal model and then
presenting the cardioid design equations to measure the
forward and reverse pressure waves. Section 3 presents
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 2 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
Rp2
p1
p+
p-
h
x
0
Fig. 1:
Model of the ear canal as a one-dimensional
transmission line, terminated at
x=0
with the
eardrum reflectance R.
a prototype microphone array and validation measure-
ments on a replica ear model, followed by discussion
and conclusions.
2 Two-Microphone Measurement
Method
2.1 Ear Canal Model
To illustrate the concepts discussed, we employ a sim-
ple model of the ear canal as a lossless straight-walled
tube with one-dimensional plane wave propagation, il-
lustrated in Figure 1. The tube is terminated at one
end by a surface with reflectance factor
R(ω)
, repre-
senting the eardrum. According to the time-harmonic
solution to the 1D wave equation in the tube [
16
], the
sound pressure
p(x,ω)
along the tube is a sum of a
forward-traveling incident wave
p+(x,ω)
and a reverse
traveling wave
p−(x,ω)
that has been reflected in the
eardrum. In the following we drop the argument
ω
for
conciseness. With the geometry defined by Figure 1,
we have
p+(x) = ˆpejkx (2)
p−(x) = ˆpRe−jkx (3)
p(x) = p+(x) + p−(x),(4)
where
ˆp
is the peak sound pressure of the incident wave,
k=ω/c,cis the speed of sound and j=√−1.
The reflectance factor
R
in the tube model can be de-
termined from sound pressure measurements at two
points along the tube, as described by the standardized
two-microphone method for determining acoustic prop-
erties of material samples in an impedance tube [
17
].
The eardrum reflectance for real ears is highly variable
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-20
-15
-10
-5
0
5
10
magnitude (dB)
p+
p-
p+ + p-
Fig. 2:
Modeled magnitude responses of the forward
and reverse pressure components in the ear
canal model, and their sum at the eardrum posi-
tion x=0.
between individuals. For the simulations in this sec-
tion we use a model for
R
that was fit approximately to
average data published in [18].
With the frequency response of the incident wave des-
ignated as being flat (
ˆp=1
), Figure 2 illustrates the
magnitude of the sound pressure components of Eqs.
(2)-(4), at the eardrum position (
x=0
). For this case,
the magnitude of the reflectance factor
R
equals the
magnitude of
p−(x)
, and can thus be read out of the
figure as well.
Figure 3(a) illustrates the strong dependency on mea-
surement position when measuring the total sound pres-
sure in the ear canal. The graph shows the simulated
sound pressure response at different points along the ear
canal model, normalized to the pressure at the eardrum
position. The interaction between the forward and re-
verse pressure waves creates a standing-wave pattern
in the ear canal, resulting in a magnitude response that
varies strongly with position.
A small displacement of the microphone can occur be-
tween subsequent measurements of HRTFs and HpTFs,
leading to coloration when evaluating Eq. (1) to design
a filter for binaural synthesis. The introduced coloration
corresponds to the magnitude response difference be-
tween the two slightly different positions along the ear
canal. Figure 3(b) shows the simulated coloration re-
sulting from a microphone displacement of 1 mm at
different original measurement points along the ear
canal. As can be seen, the coloration is substantial at
high frequencies.
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 3 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-20
-15
-10
-5
0
5
10
magnitude (dB)
x = 0mm
x = 5mm
x = 10mm
x = 15mm
x = 20mm
x = 25mm
(a)
1k 2k 5k 10k 20k
frequency (Hz)
-15
-10
-5
0
5
10
15
difference (dB)
x = 5mm
x = 10mm
x = 15mm
x = 20mm
x = 25mm
(b)
Fig. 3:
a) Simulated sound pressure magnitude response at different points along the ear canal (normalized to the
eardrum pressure), and b) relative change in magnitude response for a microphone displacement of 1 mm.
The modeled magnitude responses of the forward and
reverse pressure waves, on the other hand, are not af-
fected by standing waves and are identical for different
points along the tube model. This observation moti-
vates measurement of these pressure components in-
stead of the total sound pressure in the ear canal, for
use in filter design for individual binaural synthesis.
The proposed measurement method is outlined in the
following.
2.2 Cardioid Array Design
The forward and reverse pressure responses can be
determined from sound pressure measurements at two
points
p1=p(x1)
and
p2=p(x2)
along the tube. The
points are illustrated in Figure 1. Using Eqs. (2)-(4), a
relationship between the forward and reverse pressure
and the measurements p1and p2can be defined as
1ejkh
ejkh 1p+(x1)
p−(x2)=p1
p2.(5)
Here,
h=x2−x1
denotes the spacing between the mea-
surement points. Solving for the forward and reverse
pressure gives
p+(x1)
p−(x2)=1
1−ejk2h1−ejkh
−ejkh 1p1
p2.(6)
The above expression can be written more compactly
in terms of filters H1and H2, obtaining
p+(x1)
p−(x2)=H1H2
H2H1p1
p2(7)
where, after some algebraic simplifications,
H1
and
H2
are given by
H1=1
1−ejk2h=−e−jkh
ejkh −e−jkh =−e−jkh
2jsinkh ,
H2=−ejkh
1−ejk2h=1
ejkh −e−jkh =1
2jsinkh .
(8)
The forward and reverse pressures,
p+(x1)
and
p−(x2)
,
are calculated by filtering the measurements,
p1
and
p2
, using the filters
H1
and
H2
. A closer examination
reveals that
H1
and
H2
are identical to standard ex-
pressions used for implementing a directional pickup
pattern on a two-microphone array that approaches a
cardioid in the free field [
19
]. This is logical since
an ideal cardioid pattern has unity gain on its frontal
axis and zero gain in the opposite direction. Therefore,
depending on the orientation of the cardioid in the ear
canal, either p+(x1)or p−(x2)is measured.
The spacing
h
between the microphones must not be
selected too large. The common denominator of
H1
and
H2
becomes undefined if
sin(kh) = 0
, or equivalently if
h
equals a multiple of half a wavelength. When work-
ing with discrete-time signals, this leads to a practical
upper limit of
h<c/fs
, where
fs
is the sample rate. At
48 kHz sample rate the limit is around d<7.2 mm.
The filter gain of
H1
and
H2
is approximately propor-
tional to
1/ωh
and can become very large at low fre-
quencies when
h
is small. Large filter gain can cause
issues with signal-to-noise ratio and excessive sensi-
tivity to the precise gain matching between the micro-
phones. It is therefore not suitable to implement
H1
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 4 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
and
H2
directly. To address the gain problem, we tran-
sition the cardioid to an omnidirectional response at
low frequencies. For this, we use zero-phase low-pass
and high-pass crossover filter functions
Hlp
and
Hhp
defined as
Hlp =1
1+ (ω/ωc)N,
Hhp =1−Hl p.
(9)
Here,
ωc
is the crossover frequency, and
N
is the filter
order. As shown in Figure 3(a), the sound pressure
becomes homogeneous in the ear canal at lower fre-
quencies. The pressure components
p+(x)
and
p−(x)
are thus essentially in phase at lower frequencies and
can be approximated as
p+(x)≈p−(x)≈p(x)/2≈
(p1+p2)/4
. We obtain the final filters by applying
the cardioid filter in the high-pass branch and a scaled
sum of the microphone signals in the low-pass branch.
This gives modified filters that approximately satisfy
Eq. (7):
H0
1=Hlp /4+Hhp H1
H0
2=Hlp /4+Hhp H2.(10)
This modification helps to mitigate the gain problem
at low frequencies, while allowing estimation of
p+(x)
and p−(x)over the full frequency range.
3 Validation Measurements
Validation measurements were performed on a replica
ear using a prototype microphone array consisting of
two miniature MEMS microphones. The purpose of the
measurements was twofold: to confirm that measured
estimates of the forward and reverse pressures,
p+(x)
and
p−(x)
, are not affected by standing wave notches
and depend less on position than the total sound pres-
sure; and to test the utility of cardioid measurements in
filter design for binaural rendering. The replica ear is
made out of transparent rubber and has been cast from
a real person. It has a realistically shaped ear canal that
measures approximately 28 mm in length.
Figure 4(a) shows a picture of the replica ear and the
microphone array together with cabling and connectors,
and Figure 4(b) shows a closer view of the MEMS mi-
crophone capsules. The capsule model is CUI Devices
CMM-2718AT-3817NC-TR, chosen due to its small
footprint and adequate SNR. It is an analog, top port de-
sign. Two capsules have been glued together to form an
(a)
(b)
Fig. 4:
a) Replica ear and microphone array used for
validation measurements., b) Close-up view of
MEMS microphone array capsules.
array with a spacing of
h=2.2
mm between the ports.
The cabling uses thin 36 AWG wire and the MEMS
soldering area has been coated with an epoxy layer to
increase durability and prevent electric short-circuiting.
The total package measures 3.9x2.8x1.5 mm. The mi-
crophone array is connected to a sound card using two
XLR connectors, and a custom-designed PCB inside
the XLR connectors allows the microphones to be 48V
phantom powered from the sound card.
Cardioid filters were designed for the microphone array
according to Eqs. (8)-(10), using a crossover between
omnidirectional and cardioid response of order
N=8
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 5 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-20
-10
0
10
20
magnitude (dB)
Fig. 5:
Magnitude response of filters
H0
1
and
H0
2
for the
prototype cardioid array.
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-30
-25
-20
-15
-10
-5
0
5
magnitude (dB)
0°
90°
120°
150°
180°
Fig. 6:
Measured polar response of the prototype car-
dioid array.
and with crossover frequency 1.5 kHz. Figure 5 dis-
plays the resulting filter magnitude response. The filters
were realized as time-domain finite impulse response
(FIR) filters by taking the inverse FFT1.
The microphone capsules were calibrated to differ in
gain by less than
±0.1
dB. Figure 6 shows a measure-
ment of the resulting free-field polar response of the
microphone array. As expected, the array becomes
omnidirectional below the crossover frequency and
approaches a unidirectional response at high frequen-
cies. In line with the reasoning in section 2.2, the
free-field array response is down 6 dB at low frequen-
cies to compensate for the array responding to only
"half" the sound pressure in the ear canal above the
1
after adding a suitable modeling delay and a windowed-sinc
low-pass filter near the Nyquist frequency to the filter equations.
crossover frequency (
p+
or
p−
) but the total sound
pressure (p++p−) below it.
In section 3.1 below we compare cardioid array and
single microphone measurements at different points in
the ear canal of the replica ear. Then, in section 3.2,
we investigate the error in reproduced sound pressure
at the eardrum position of the replica ear, when head-
phones are used to reproduce a measured binaural room
impulse response (BRIR).
3.1 Measurements at Different Ear Canal
Positions
The pressure components
p+(x)
,
p−(x)
, and total
sound pressure
p1(x)
were measured at 5 mm intervals
in the ear canal of the replica ear. For these measure-
ments, the replica ear was placed at the edge of a table
in a normally reflective room, and impulse responses
were measured from a Genelec 8341-series coaxial
speaker to the microphone array in the ear canal. The
speaker was placed at a distance of 70 cm and at a sim-
ilar height as the ear, and at an azimuth angle of 45
◦
from the frontal axis of the ear. A logarithmic sine
sweep was used as measurement signal, and the cap-
tured impulse responses were windowed to 4 ms length
to simulate free-field conditions2.
The sound field pressure components were estimated ac-
cording to Eq. (7). The resulting magnitude responses,
with 1/8-octave smoothing applied, are presented in
Figure 7. Figure 7(a) shows the measured response
of the total sound pressure
p1(x)
, normalized by the
"eardrum" sound pressure
p1(0)
. The impact of stand-
ing waves on
p1(x)
is large, as predicted by the simu-
lation in Figure 3. The notches are deeper than in the
simulation because the reflectance at the termination of
the replica ear canal is higher than in an average real
ear.
Figures 7(b) and 7(c) show the measured estimates of
p+(x)
and
p−(x)
, respectively, again normalized by
p1(0)
. Effects of standing waves are much reduced in
the measured
p+(x)
and
p−(x)
and the spread between
the curves for the different measurement positions is
much smaller than for the total pressure
p1(0)
. The
measurements of
p+(x)
and
p−(x)
at the outermost po-
sition at 25 mm from the eardrum have somewhat more
2
The loss of low-frequency information due to windowing has
a negligible impact on the following analysis which only considers
relative spectral differences.
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 6 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-30
-25
-20
-15
-10
-5
0
5
magnitude (dB)
x=0 mm
x=5 mm
x=10 mm
x=15 mm
x=20 mm
x=25 mm
(a) p1(x)/p1(0)
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-30
-25
-20
-15
-10
-5
0
5
magnitude (dB)
(b) p+(x)/p1(0)
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-30
-25
-20
-15
-10
-5
0
5
magnitude (dB)
(c) p−(x)/p1(0)
Fig. 7:
a) Measured sound pressure
p1(x)
at differ-
ent points in the ear canal of the replica ear,
b) Measured forward pressure
p+(x)
,c) Mea-
sured reverse pressure
p−(x)
. All curves are
normalized by the pressure response
p1(0)
at
the eardrum reference position.
magnitude response ripple than for the other positions.
In practice, measurement positions past the first bend
of the ear canal may be preferable to measurements at
100 200 500 1k 2k 5k 10k 20k
frequency (Hz)
-30
-25
-20
-15
-10
-5
0
5
magnitude (dB)
p1
2p+
2p-
Fig. 8:
Measured magnitude response of sound pres-
sure components at 15 mm from the eardrum
position, normalized by the pressure response
p1(0)at the eardrum position.
the ear canal entrance.
3.1.1 Comments on Measurements
In the transmission-line ear canal model discussed in
section 2.1, the forward and reverse pressure magnitude
response is independent of position. A real ear canal
has a varying cross-sectional area along its length and
tapers off toward the eardrum, and can be more accu-
rately modeled as an acoustic horn [
20
]. The measured
responses in Figure 7 tend to fall off at high frequen-
cies for measurement positions farther away from the
eardrum position, which is consistent with published
results on the spatial distribution of sound pressure in
the human ear canal [20].
Figure 8 shows a comparison between the measured to-
tal, forward, and reverse pressure magnitude responses
15 mm from the eardrum position using the same data
as in Figure 7. The standing wave notches are largely
absent from the forward and reverse pressure responses.
Some remaining ripple in the measured
p+(x)
and
p−(x)
might be related to an imperfect separation of
the forward and reverse pressure waves due to, for ex-
ample, imperfect microphone calibration. Also, the
response of the cardioid microphone array depends
on its alignment with the length axis of the ear canal,
which is difficult to control exactly.
3.2 Error in Reproduced Sound Pressure at the
Eardrum
A second series of measurements were performed to
verify the use of cardioid array measurements in fil-
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 7 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
1k 2k 5k 10k 20k
frequency (Hz)
-10
-5
0
5
10
magnitude error (dB)
Single mic.
Cardioid
Fig. 9:
Magnitude response error in reproduced sound
pressure at the eardrum position of the replica
ear, in example filter design for binaural ren-
dering. Comparison between filters based on
cardioid and single microphone measurements.
ter design for binaural rendering. The replica ear was
mounted in a jig made out of medium-density fiber-
board that allowed a pair of headphones to be placed
over it. A third miniature MEMS microphone was
placed at the eardrum position of the replica ear and
the two-microphone array was placed at around 18 mm
from the eardrum position.
A BRIR was measured simultaneously with the three
microphones, with the Genelec speaker at around
50 cm distance. After the BRIR measurement, the
two-microphone array was intentionally moved around
1 mm outward in the ear canal. Next, a pair of
Sennheiser HD600 headphones was put over the ear,
and the headphone response (HpTF) was measured
with the three microphones. This allowed the design of
a filter for headphone rendering of the BRIR according
to Eq. (1), by replacing the HRTF in the numerator
with the frequency-domain equivalent of the measured
BRIR, i.e., the measured binaural room transfer func-
tion (BRTF).
Three filters were designed: one based on the BRTF and
HpTF measured at the eardrum position, designated as
the reference filter (
Hre f
v
); a second filter,
Hc
v
, based
on the cardioid measurements; and a third filter,
Hm
v
,
using measurements by the single inner microphone in
the two-microphone array. To assess the reproduction
error at the eardrum when using
Hc
v
and
Hm
v
for bin-
aural rendering, we calculated
Hc
v/Hre f
v
and
Hm
v/Hre f
v
,
respectively. Figure 9 displays the reproduction error
for the two filters.
Figure 9 shows that the shift in microphone position
between the BRTF and HpTF measurement resulted in
large coloration with sharp magnitude response peaks
in the filter based on single microphone measurements.
In contrast, the filter based on cardioid measurements
reproduces sound pressure at the eardrum position with
high accuracy. In a real ear, the single microphone case
would likely exhibit somewhat lower but still signifi-
cant coloration due to lower eardrum reflectance than
that of the replica ear, c.f. Figure 3(b).
4 Discussion
The validation measurements in the previous section
suggest that measurements of
p+(x)
or
p−(x)
are suit-
able for use in filter design problems for binaural syn-
thesis, due to their relative insensitivity to variation
in the measurement position. The absence of stand-
ing wave notches in the measurements can also make
inverse filter design for headphone correction better
conditioned. The forward pressure
p+(x)
typically has
a slightly higher level than the reflected reverse pres-
sure
p−(x)
, and may therefore be preferred from an
SNR perspective.
The forward pressure level has previously been sug-
gested for use e.g. in connection with the fitting of
hearing aids, to avoid the influence of standing waves
on measurements in the ear canal [
10
]. A conventional
procedure for calculating the forward pressure is model-
based and relies on a single sound pressure measure-
ment in the ear canal with an earphone probe, together
with knowledge of the Thévenin-equivalent acoustic
impedance and pressure of the sound source. A benefit
of the method presented here is that it does not require
estimation of any model parameters and can be used
both for free-field measurements and with headphones
of different types.
There are several methods that could be used to es-
timate sound pressure at the eardrum from the two-
microphone measurement. One is to sum
p+(x)
and
p−(x)
with appropriate time alignment. The energy-
based method of Hiipakka et. al. can also be an alterna-
tive [
13
], seeing that acoustic particle velocity can be
estimated from two closely spaced microphones [
16
].
However, this topic is left for future research.
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 8 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
The proposed two-microphone method naturally adds
some additional complexity over traditional single-
microphone binaural measurements. Further research is
needed to demonstrate the practicality of the proposed
method for measurements on real ears and to investi-
gate practical filter design cases for binaural rendering.
Sensitivity to microphone calibration mismatch and its
effect on the measurements should also be investigated.
5 Summary
A method for measuring the forward and reverse pres-
sure components with a cardioid microphone array in
the ear canal was presented. The technique is suitable
to use for measuring HRTFs and HpTFs with an open
ear canal. Compared to the blocked-canal method, open
ear canal measurements are useful for designing filters
for binaural rendering that do not require headphones
with special FEC properties.
Validation measurements in a replica ear confirm that
the measured forward and reverse pressures are largely
unaffected by standing wave notches and show much
less positional dependence than the total pressure in
the ear canal. This indicates that the proposed measure-
ment technique is more robust to accidental variations
in the microphone position during the measurements,
which implies lower error and higher fidelity in filter
design for binaural rendering.
References
[1]
Wightman, F. L. and Kistler, D. J., “Headphone
simulation of free-field listening. I: Stimulus
synthesis,” The Journal of the Acoustical Soci-
ety of America, 85(2), pp. 858–867, 1989, doi:
10.1121/1.397557.
[2]
Brinkmann, F., Lindau, A., and Weinzierl, S., “On
the authenticity of individual dynamic binaural
synthesis,” The Journal of the Acoustical Society
of America, 142(4), pp. 1784–1795, 2017, doi:
10.1121/1.5005606.
[3]
Griesinger, D., “Laboratory Reproduction of Bin-
aural Concert Hall Measurements through Indi-
vidual Headphone Equalization at the Eardrum,”
in 142nd Convention of the Audio Engineering
Society, 2017.
[4]
Møller, H., “Fundamentals of binaural technol-
ogy,” Applied Acoustics, 36, pp. 171–218, 1992.
[5]
Møller, H., Sørensen, M., Jensen, C., and Ham-
mershøi, D., “Binaural technique: Do we need
individual recordings?” The Journal of the Audio
Engineering Society, 44(6), pp. 451–464, 1996.
[6]
Møller, H., Hammershøi, D., Jensen, C. B., and
Sørensen, M. F., “Transfer Characteristics of
Headphones Measured on Human Ears,” Jour-
nal of the Audio Engineering Society, 43(4), pp.
203–217, 1995.
[7]
Pralong, D. and Carlile, S., “The role of individu-
alized headphone calibration for the generation of
high fidelity virtual auditory space,” The Journal
of the Acoustical Society of America, 100(6), pp.
3785–3793, 1996, doi:10.1121/1.417337.
[8]
Engel, I., Alon, D. L., Robinson, P. W., and
Mehra, R., “The Effect of Generic Headphone
Compensation on Binaural Renderings,” in AES
International Conference on Immersive and Inter-
active Audio, 2019.
[9]
Hammershoøi, D. and Møller, H., “Sound trans-
mission to and within the human ear canal,”
The Journal of the Acoustical Society of Amer-
ica, 100(1), pp. 408–427, 1996, doi:10.1121/1.
415856.
[10]
McCreery, R. W., Pittman, A., Lewis, J., Neely,
S. T., and Stelmachowicz, P. G., “Use of forward
pressure level to minimize the influence of acous-
tic standing waves during probe-microphone
hearing-aid verification,” The Journal of the
Acoustical Society of America, 126(1), pp. 15–24,
2009, doi:10.1121/1.3143142.
[11]
Li, S. and Peissig, J., “Measurement of Head-
Related Transfer Functions: A Review,” Applied
Sciences, 10(14), pp. 1–40, 2020, doi:10.3390/
app10145014.
[12]
Møller, H., Sørensen, M. F., Hammershøi, D.,
and Jensen, C. B., “Head-Related Transfer Func-
tions of Human Subjects,” Journal of the Audio
Engineering Society, 43(5), pp. 300–321, 1995.
[13]
Hiipakka, M., Kinnari, T., and Pulkki, V., “Es-
timating head-related transfer functions of hu-
man subjects from pressure–velocity measure-
ments,” The Journal of the Acoustical Society
of America, 131(5), pp. 4051–4061, 2012, doi:
10.1121/1.3699230.
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 9 of 10
Gunnarsson and Smailagi´
c Two-Microphone Array for Binaural Measurements
[14]
de Bree, H.-E., “An Overview of Microflown
Technologies,” Acta Acustica united with Acus-
tica, 89, pp. 163–172, 2003.
[15]
Takanen, M., Hiipakka, M., and Pulkki, V., “Au-
dibility of Coloration Artifacts in HRTF Filter
Designs,” in AES 45th International Conference:
Applications of Time-Frequency Processing in Au-
dio, 2012.
[16]
Blackstock, D. T., Fundamentals of physical
acoustics, Wiley, New York, 2000, ISBN 978-
0-471-31979-5.
[17]
ISO-10534-2:1998, Acoustics — Determination
of sound absorption coefficient and impedance
in impedance tubes — Part 2: Transfer-function
method, International Organization for Standard-
ization, Geneva, Switzerland, 1998.
[18]
Nørgaard, K. M., Fernandez-Grande, E.,
Schmuck, C., and Laugesen, S., “Reproducing
ear-canal reflectance using two measurement tech-
niques in adult ears,” The Journal of the Acous-
tical Society of America, 147(4), pp. 2334–2344,
2020, doi:10.1121/10.0001094.
[19]
Olson, H. F., “Gradient Microphones,” The Jour-
nal of the Acoustical Society of America, 17(3),
pp. 192–198, 1946, doi:10.1121/1.1916315.
[20]
Stinson, M. R. and Daigle, G. A., “Comparison of
an analytic horn equation approach and a bound-
ary element method for the calculation of sound
fields in the human ear canal,” The Journal of the
Acoustical Society of America, 118(4), pp. 2405–
2411, 2005, doi:10.1121/1.2005947.
AES International Conference on Spatial and Immersive Audio, Huddersfield, UK, 2023 August 23–25
Page 10 of 10
