The impact of early reflections on binaural cues
and Romain Brette
Equipe Audition, De´ partement d’Etudes Cognitives, Ecole Normale Supe´rieure, 29, rue d’Ulm,
75005 Paris, France
(Received 14 June 2011; revised 16 May 2012; accepted 16 May 2012)
Animals live in cluttered auditory environments, where sounds arrive at the two ears through
several paths. Reﬂections make sound localization difﬁcult, and it is thought that the auditory
system deals with this issue by isolating the ﬁrst wavefront and suppressing later signals. However,
in many situations, reﬂections arrive too early to be suppressed, for example, reﬂections from the
ground in small animals. This paper examines the implications of these early reﬂections on binaural
cues to sound localization, using realistic models of reﬂecting surfaces and a spherical model of
diffraction by the head. The fusion of direct and reﬂected signals at each ear results in interference
patterns in binaural cues as a function of frequency. These cues are maximally modiﬁed at
frequencies related to the delay between direct and reﬂected signals, and therefore to the spatial
location of the sound source. Thus, natural binaural cues differ from anechoic cues. In particular,
the range of interaural time differences is substantially larger than in anechoic environments.
Reﬂections may potentially contribute binaural cues to distance and polar angle when the properties
of the reﬂecting surface are known and stable, for example, for reﬂections on the ground.
C2012 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4726052]
PACS number(s): 43.20.El, 43.66.Pn, 43.66.Qp [MAA] Pages: 9–27
To localize sound sources, many species, including
humans, rely on subtle differences in the signals arriving at
the two ears. The ear closer to the source receives the sound
earlier and with a higher level than the other ear. These inter-
aural time differences (ITDs) and interaural level differences
(ILDs) are produced by sound propagation and diffraction of
sounds by the head, pinnae, and body. They vary systemati-
cally with the location of the sound source. The relationship
between these binaural cues and sound location have been
described in many species, mainly using acoustical measure-
ments of head-related transfer functions (HRTFs) in anechoic
chambers, in order to minimize the disturbances due to reﬂec-
tions. However, the acoustical environments animals live in
contain many objects that produce reﬂections, such as trees,
natural or artiﬁcial walls, and the ground. Even in the open
air, with no obstacle, at least one reﬂection is produced by
the ground, and its texture can be very variable, e.g. grass,
snow, soil, or asphalt. In principle, these reﬂections can affect
binaural cues, as pointed out by McFadden (1973).
Nevertheless, humans can maintain good localization
and segregation abilities in echoic environments (Blauert,
1997;Freyman et al., 2001;Litovsky et al., 1999;Zurek,
1987). This robustness to reﬂections is thought to be medi-
ated by the precedence effect (Litovsky et al., 1999). When a
sound and a reﬂection are separated by less than 1 ms, a
fused sound is perceived, with an intermediate localization
(summing localization). When the delay to the reﬂection is
between about 1 and 5 ms, the perceived source location is
dominated by the location of the leading sound - this prop-
erty is called the “law of the ﬁrst wavefront” (Blauert, 1997;
Shinn-Cunningham et al., 1993;Wallach et al., 1949). When
the delay is longer than about 5–10 ms, the two sounds
become separately audible (breakdown of fusion) and their
two distinct localizations are perceived. Note that the break-
down of fusion is longer (50 ms) for speech or music than
for transient sounds (Litovsky et al., 1999;Lochner and
Similar ﬁndings have been reported in a number of spe-
cies, with delays in the same range: cats (Cranford, 1982;
Populin and Yin, 1998), rats (Kelly, 1974), crickets (Wytten-
bach and Hoy, 1993), owls (Keller and Takahashi, 1996a;
Spitzer and Takahashi, 2006), and birds (Dent and Dooling,
2004). For example, in cats, localization performance
degrades for delays below 0.5 ms, which is consistent with
summing localization (Cranford, 1982;Populin and Yin,
1998;Tollin and Yin, 2003). Neural correlates of the prece-
dence effect have also been seen in recordings in the inferior
colliculus and auditory cortex of cats: for example, with
clicks separated by more than 2 ms, neural responses to the
lagging click are suppressed (Dent et al., 2009;Mickey and
Middlebrooks, 2001;Yin, 1994).
Thus, many reﬂections are either suppressed or sepa-
rately processed by the auditory system. However, not all
reﬂections can be suppressed by the auditory system. Con-
sider the situation illustrated in Fig. 1. The animal faces a
sound source, with its ears at a distance pfrom the ground.
Two signals arrive at the animal: the direct sound and its
reﬂection at the ground. Since the shortest path between two
points is a straight line, the path length of the reﬂection can
be no more than the distance from the sound source plus 2p
(see Fig. 1). Thus, the time delay of the reﬂection is always
Current address: Centre de Neurosciences Paris-Sud (CNPS), UMR CNRS
8195, Universite´ Paris-Sud, Baˆ timent 446, rue Claude Bernard, 91405
Orsay Cedex, France.
Author to whom correspondence should be addressed. Also at: Laboratoire
Psychologie de la Perception, CNRS, Universite´ Paris Descartes, 45, rue des
Saints-Pe`res 75006 Paris, France. Electronic mail : firstname.lastname@example.org
J. Acoust. Soc. Am. 132 (1), July 2012 V
C2012 Acoustical Society of America 90001-4966/2012/132(1)/9/19/$30.00
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shorter than 2p=c, where c343 m=s is the speed of sound
in air at 20 C. For example, for a guinea pig, which is about
8 cm tall, this delay is always shorter than 250 ls for all
sounds produced on the horizontal plane. This is well within
the range when the two sounds are perceptually fused.
Therefore, the binaural cues that are available to the animal
should be heavily affected by reﬂections. This hypothesis is
supported by real recordings of ILDs in gerbils after reﬂec-
tion by a plywood ﬂoor, which show interference patterns
(Maki et al., 2003).
In this paper, we ﬁrst examine early reﬂections in simple
geometrical models to understand how likely they are to pro-
duce reﬂected waves within the “fusion” range for several
species (Sec. II). We then examine the impact of these
reﬂections on binaural cues, ﬁrst when diffraction is absent
(Sec. III A), and then using a spherical head model with real-
istic models of natural textures (Sec. III B). We ﬁnd that
ILDs are more modiﬁed than ITDs, and that the variation in
ITD can be systematically related to the distance and polar
angle from the source (Sec. IV), potentially providing a
localization cue. We also notice that variations of ITDs and
ILDs due to reﬂections substantially extend the range of bin-
aural cues that the auditory system has to manage (Sec. V).
Finally, we discuss the implications of these results for
neural coding of sound location, binaural localization cues,
and psychophysical experiments.
II. EARLY REFLECTIONS AND THE PRECEDENCE
We consider two simple situations describing the proxim-
ity of a human or an animal to the ground or to a wall (Fig. 2).
Let Sbe a sound source at distance dfrom the head. In the
spherical coordinate system typically used in localization
studies, Shas a lateral angle (azimuth) u
and a polar angle
(elevation, latitude) h
relative to the center of the head (see
Appendix Afor all symbols). When the sound wave propagat-
ing from Sencounters an obstacle such as the ground [Fig.
2(A)] or a wall [Fig. 2(B)], it is partly reﬂected and partly
absorbed. The incidence angle of the reﬂected sound wave is
that of a source S* which “mirrors” Srelative to the obstacle.
As a consequence, for a reﬂection at the ground, the reﬂected
and direct sound waves have the same lateral angle; for a
reﬂection at a vertical wall, they have the same polar angle.
In the case of a reﬂection at the ground, the path length
d* of the reﬂection is, at most, the distance of the sound
source dplus 2p(see Fig. 1). Therefore the delay of the
reﬂected sound is no more than 2p/c. This upper bound cor-
responds to the case when the source is directly above the
head (i.e., polar angle ¼90), but in many natural situa-
tions, this delay is shorter, in particular if the source is far
from the ears or close to the ground. This is illustrated in
Fig. 3, which shows the computed delay between direct and
reﬂected sounds as a function of the distance from the
source to head and the polar or lateral angle of the sound
source to the head (see Appendix Bfor the calculations).
For the situation of a zero polar angle, when the source is
farther than 10 m then this delay is less than 0.15 ms for ani-
mals smaller than cats [Fig. 3(B)], and less than 1 ms for
humans [Fig. 3(A)]. The same reasoning applies to a reﬂec-
tion from a wall, where the distance to the ground is
replaced by the distance to the wall.
More generally, consider a source and a receiver at dis-
tance dfrom each other. The set of reﬂection points such
FIG. 1. (Color online) The maximum difference in path length between the
direct and reﬂected sound. The source is at distance dfrom the ears, which
are at height pfrom the ground. The direct path length is d(solid black
line), and the reﬂected path (dashed black line) is shorter than the dotted
path, which has length dþ2p. Thus, the difference in path length is always
smaller than 2p.
FIG. 2. (Color online) Geometrical models of reﬂections. Panels A and B show two basic models of sound reﬂections by the ground and a wall. The polar
angle (A) or lateral angle (B) of the sound source is u
(A) or h
(B) and that of the reﬂected sound is u
(A) or h
(B): pis the distance between the ears and
the obstacle. d* is the reﬂected path length. Panel C shows, for ﬁxed locations of the source and receiver, that the set of reﬂection points on the horizontal plane
that produce a ﬁxed delay D¼(d*d)=cforms an ellipse with foci at the source and receiver.
10 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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that reﬂected path length is a ﬁxed quantity d* is an ellipse
with foci at the source and receiver [Fig. 2(C)]. In three di-
mensions, this would be an ellipsoid. All obstacles that are
tangent to this ellipse produce reﬂections with delay
D¼(d*d)=c. For example, delays shorter than D¼1ms
are produced by all objects within an ellipse that pass
through the two external points aligned with the source and
receiver at distance Dc=2¼17 cm from them [Fig. 2(C)].
In Table I, we have listed the maximum delay for a
reﬂection at the ground for various different species as well
as the values of the delays when the source is 1.5 m away
from the ears. For a human, for whom the average distance
between ears and ground is 1.7 m, the reﬂected waves are
often delayed by several milliseconds [for example, it is
6.5 ms at a distance of 1.5 m; Fig. 3(A)]. This is within the
range of echo suppression in the precedence effect. But the
ears of small mammals such as guinea pigs or gerbils are
only a few centimeters away from the ground. For instance,
even if the gerbil decides to stand up to view its environ-
ment, it is only 12 cm high in this fully erect posture, which
means a maximum delay of 730 ls for a reﬂection at the
ground. This upper bound corresponds to the situation where
the source is at a polar angle of 90, but when the source is
at a polar angle of 0, i.e. at the same height as the animal,
the delay is generally much shorter because the sound hits
the ground with grazing incidence. This makes the reﬂected
path length very close to the direct path length geometri-
cally. For example, the delay is only 56 ls for a source at
FIG. 3. The computed delay in milliseconds between the direct and the ground-reﬂected (panels A, B) or wall-reﬂected (panels C, D) sound waves as a func-
tion of the distance from the head and polar angle (A, B) or lateral angle (C, D) of the source. The ground is assumed to be at a distance of p¼1.7 m (A) or
p¼0.2 m (B) from the head. The hatched area represents the geometrically impossible cases where the source would be below the ground. The contours for
different delays are shown as dashed lines.
TABLE I. The computed time delay between the front and reﬂected sound waves using a ground reﬂection model for typical ear-ground distances in several
species (top line), and for two different source-ground distances (equivalently, two different polar angles).
Ear-ground 1.70 0.75 0.4 0.2 0.12 0.08 0.02
distance (m) (at most)
wave delay (ms)
Maximum delay (ms) 10.3 4.5 2.4 1.2 0.73 0.48 0.12
dist.: 1.5 m elev.: 0(source
height ¼ear-ground distance)
6.5 1.82 0.58 0.154 0.056 0.025 0.0016
dist.: 1.5 m 4.62 2.3 1.3 0.66 0.39 0.26 0.07
source height ¼1 m (elev. in
) (22) (28) (30) (32) (33)
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 11
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1.5 m from the gerbil. In addition, because they are small,
these mammals often move with their ears close to reﬂecting
surfaces, such as embankment slopes. Even for cats (about
20 cm high), the delays are shorter than 1.2 ms in all conﬁgu-
rations, and shorter than 1 ms in most natural cases [Fig.
3(B), white line]. Even if the fusion threshold were lower for
small mammals than for humans, short delays such as 56 ls
are very likely to fall below their fusion threshold. There-
fore, the precedence effect cannot account for the processing
of early reﬂections in ecological situations for small mam-
mals. Instead, the binaural cues that are available to these
animals should include the impact of early reﬂections. For
this reason, we now focus on small mammals, but we shall
come back to the case of humans in the discussion.
III. IMPACT OF REFLECTIONS ON BINAURAL CUES
A. A simple case: Rigid surface and no diffraction
We start by considering an elementary situation with a
reﬂection at a rigid surface but no diffraction effects by the
head or similar obstacle. We also neglect the attenuating
effect of distance. Our treatment is similar to Sec. 3.1 in
Blauert, 1997 (“phasor diagrams” in Fig. 3.8), which also
includes a few relevant references such as Leakey (1959)
and Wendt (1963). Suppose the source signal is a pure tone
with frequency f, which we represent as a complex signal
e2pift. The ear receives the sum of the direct sound (delay d)
and reﬂected sound (delay d*):
which is proportional to ð1þe2pifDÞ, where D¼d*dis
the delay of the reﬂection to the direct sound. This results in
an interference which may be constructive (fD¼n,nbeing
an integer) or destructive ( fD¼nþ1=2) [see Fig. 4(A)].
More precisely, for a ﬁxed delay D, the level and phase of
the summed signal are periodic functions of the tone fre-
quency f, with spectral period 1=D. At the frequency of each
destructive interference [ f¼1=(2D)þn=D], the level drops
to 0 (i.e., 1 dB), but more interestingly the phase abruptly
shifts from p=2top=2 [see Fig. 4(B)]. This corresponds to
a sign change in the summed vector near the interference
We now examine the impact of monaural interferences on
binaural cues. In the case of a vertical wall, the delay between
the direct and reﬂected sounds is not the same at the two ears
[see Fig. 4(C)]. The signal at the left ear is proportional to
and the signal at the right ear is proportional to
SRðtÞ/ð1þe2pifDRÞe2pi f ITD:(3)
Thus, to understand the consequences on binaural cues, we
need to compare the vectors ð1þe2pif DLÞand ð1þ
e2pif DRÞ[see Fig. 4(D)]. Assuming that the two delays are
similar (i.e., D
), the interaural phase difference (IPD)
and the ILD are approximately periodic functions of f, with
spectral period D(D
)=2. As in the monaural case,
two things occur at the frequencies of destructive interfer-
ILD goes to 61, and the IPD changes discontinuously.
Between the interference frequencies, the IPD change due to
the interferences is close to p. Thus, interferences cause
large variations in ILD and discontinuities in IPD.
In the case of a reﬂection at the ground, the delays D
are also slightly different. For example, consider a
sound source at polar angle 0and lateral angle 90[see
Fig. 4(E)]. If dis the distance between the sound to the left
ear and lis the interaural distance, then D
This is a small difference, except for very close sources, and
therefore the IPD and ILD should not be very degraded in
general. However, interferences are still present and cause
large changes in ILD and discontinuities in IPD near
f¼1=(2D)þn=D, as for a reﬂection at the wall [see Fig.
4(F)]. In particular, the IPD changes by pnear interference
Thus in this simple situation, we predict that with a
reﬂection the change in IPD and ILD should be a periodic
FIG. 4. (Color online) The effect of a reﬂection on binaural cues in a simple
case: An acoustically transparent head. Panel A shows that, for a pure tone of
frequency f, the interference between the direct and reﬂected sound is con-
structive when the delay is D¼n=f(top), and destructive when D¼
n=fþ1=2 (bottom). The two signals can be represented as unit vectors on a
circle (right), where the angle represents the phase of the reﬂected sound
(dashed black line, “reﬂected”) relative to the direct sound (solid gray arrow).
The total signal is the vector sum (dashed line, “total”). Its angle is therefore
the phase of the total signal and its length is its amplitude. A short arrow
would correspond to a destructive interference. When the phase of the
reﬂected sound goes beyond p(panel B), the phase of the total signal jumps
from p=2top=2 (panel B). With a reﬂection at a wall (panel C), the delay
between direct and reﬂected sounds at the left ear (solid arrow) is different
from that at the right ear (dashed arrow). Thus, in panel D, the phase of the
reﬂected sound for the left and right ears, relative to the direct sounds, are
represented by distinct solid and dashed black arrows, respectively (left). The
IPD change due to the reﬂection is the angle between the two summed vec-
tors. It changes discontinuously when the phase of one monaural signal
exceeds p(right). With a reﬂection at the ground (panel E), the delays
between reﬂected and direct sounds are similar but not exactly equal at the
left and right ear (solid and dashed thick lines, respectively). Panel F shows
that the IPD change due to the reﬂection is generally small (left), except
when a discontinuity occurs, when the phase of one monaural signal exceeds
12 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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function of frequency with spectral period 1=D, with maxi-
mal changes at the frequencies of destructive interferences: f
¼1=(2D)þn=D. We now consider more realistic models of
the auditory environment.
B. Natural surfaces and diffraction effects
1. Natural surfaces
An incident wave on a real surface is partly reﬂected and
partly absorbed in a way that depends on incidence and fre-
quency. We describe reﬂections at the ground (the equations
are equivalent for a vertical wall if polar angle uis replaced
by the lateral angle h). As before, we assume that the re-
ceiver is at distance dfrom the source and at distance d*
from the mirrored source, and we assume that the sound
wave is an isotropic spherical wave propagating outward
from a central point. The most widely used approach to
match the boundary conditions for such a wavefront imping-
ing on a plane ﬁnite-impedance surface is the Weyl–Van der
Pol solution (Sutherland and Daigle, 1998), where the sound
ﬁeld at the receiver can be expressed as the sum of direct and
reﬂected sound ﬁelds. If we deﬁne P(d, f) as the complex
pressure amplitude at frequency fand distance dfrom the
source (in the absence of reﬂecting surfaces), then the sound
at the receiver is well approximated by the equation
where Qis a spherical reﬂection factor, a complex-valued
function of frequency, angle and distance. The reﬂected
sound ﬁeld Qðd;f;uSÞPðd;fÞdepends on the polar
angle uS, the distance d* (because of the spherical wave hy-
pothesis) and the acoustic properties of the two media (air
and ground), which are frequency dependent. Detailed for-
mulae can be found in Appendix C. Many models have been
used to describe these acoustic properties for typical outdoor
surfaces. We used the Delany–Bazley model (Delany and
Bazley, 1970;Miki, 1990), where these properties are
described with a single parameter, the effective ﬂow resistiv-
ity r. In Appendix C, we list typical values for a number of
natural textures (from Cox and D’Antonio, 2009): high
values correspond to rigid surfaces (e.g., concrete) while low
values correspond to soft textures (e.g., snow).
Figure 5(A) illustrates the general properties of reﬂec-
tions on natural surfaces. When the ground is soft, a low fre-
quency wave can partially penetrate the surface, which
delays the reﬂected wave. At higher frequencies, the incident
sound is partly absorbed and the delay is shorter. The absorp-
tion and delay effects are reduced for more rigid surfaces,
i.e., those with a higher resistivity r. With a grazing inci-
dence, the reﬂection is greater and the delay is longer. These
properties are also shown in Figs. 5(B) and 5(C) for two inci-
dence angles and two natural grounds: grass (r¼10
) and sand (r¼610
Pa s m
As in the simple situation described in Sec. III A, the
direct and reﬂected waves interfere and produce large varia-
tions in level as a function of frequency [see Fig. 6(A)].
Quantitatively, these are not as large as with a rigid surface
because the reﬂections are partly absorbed. Let us ﬁrst con-
sider a realistic reﬂecting surface with reﬂection factor Q(f)
and neglect diffraction effects. The pressure decreases with
distance as 1=d. Thus the total pressure at the ear for a pure
tone at frequency fis proportional to
where s(f) is the phase delay, in seconds, of Q(f). Thus, level
and phase vary approximately periodically with frequency,
FIG. 5. (Color online) The acousti-
cal properties of natural surfaces.
Panel A shows that low frequencies
penetrate a porous surface deeper
than high frequencies, which pro-
duces a delay Din the reﬂected
sound. Panel B and C show the am-
plitude and phase delay of Q, respec-
tively, as a function of frequency
(for a sine tone) and for two values
of ﬂow resistivity r. Two incidence
polar angles are used (10,80
are indicated on each curve. The dis-
tance between source and receiver is
assumed to be d¼1.5 m.
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 13
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with spectral period 1=D. The reﬂection factor Q(f) varies
somewhat with frequency, and determines the spectral enve-
lope in Fig. 6(A). The relative amplitude of the interference
pattern varies between
with a ﬁrst minimum at frequency f
))). For a
hard surface, this is close to f
In Table II, we report the simple estimates f
for the ﬁrst interference frequency and f
¼1=Dfor the spec-
tral period, and compare them to the accurate values derived
from Eq. (5), for a rigid surface (i.e., r¼1). It can be seen
that the simple estimate of the spectral period f
is very accu-
rate for high r, while the ﬁrst interference frequency f
seems to be slightly overestimated. These estimates become
less accurate as rdecreases, i.e., for more porous surfaces.
This is to be expected since porous surfaces introduce an
FIG. 6. (Color online) The pressure after a reﬂection by a ground or a wall for a point source. Panel A shows the pressure at the receiver if there were no head
and therefore no diffraction. The geometrical parameters of the source following the conventions of Fig. 1are indicated at the top left. The parameters of the
ground- or wall-reﬂected wave are shown within the plots. Panels B and C show the pressure at the left and right ears after ﬁltering by the HRTFs of the sphere
model, for the ground (B) and wall (C) reﬂection models. The geometrical parameters of the source are the same as in (A).
TABLE II. Computed values found in the spectra shown in Fig. 6(A) and
¼1=(2D) for the ﬁrst interference frequency and f
the spectral period (see Secs. III A and III B).
First notch Computed value r¼10
1179 Hz 2051 Hz
Computed value r¼6.10
1418 Hz 2878 Hz
Estimate (r¼1) 1590 Hz 3624 Hz
Spectral Period Computed value r¼10
3103 Hz 6606 Hz
Computed value r¼6.10
3151 Hz 6942 Hz
Estimate (r¼1) 3180 Hz 7248 Hz
14 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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additional delay in low frequencies because of the properties
of the reﬂection factor Q(see Fig. 5).
2. Diffraction effects
The second aspect that we must take into account is the
diffraction of sounds by the head. This effect is described by
head-related transfer functions (HRTFs). The HRTF is the
pressure at the ear divided by the reference free-ﬁeld pres-
sure at the center of the head, for a source at a given loca-
tion. The head scatters sound waves in a way that depends
on the incidence of the wave relative to the head and the
sound frequency, and therefore HRTFs are functions of fre-
quency, distance, lateral angle, and polar angle. For a sine-
tone frequency f, we can thus deﬁne HRTFs with reﬂections
using the Weyl–Van der Pol equation described above:
Hrecðd;f;ðhS;uSÞÞ ¼ Hðd;f;ðhS;uSÞÞ
The HTRF for the left and right ears will be denoted HLand
HR, respectively. In the following calculations, we use a
spherical head model with shifted ears, for which the diffrac-
tion function is completely known and has been extensively
described, for instance, in (Duda and Martens, 1998;Ono
et al.,2008). Details are given in Appendix D.Thegeometri-
cal properties of the spherical head model were chosen to give
a match to the shape of a guinea pig head, with ears at the
back and top: a head radius of 2cm and ears at a lateral angle
of 6110and a polar angle of þ30. The head was assumed
to be at p¼8 cm from the ground or wall, corresponding to
the average distance between ears and ground in guinea pigs.
The results are shown in Figs. 6(B) and 6(C). As can be
seen, the monaural interference patterns are qualitatively simi-
lar when diffraction effects are introduced. However, these
introduce additional delays which must be taken into account
in our estimates of f
. Indeed, for the right ear, head ﬁl-
tering introduces a phase shift /S
for the direct wave and /S
the reﬂected wave. The phase difference /S
to the phase of the reﬂection wave in Eq. (1). Thus, the ﬁrst
minima in the sound spectrum at the right ear should occur at
such that 2pf0Dþ2pf0sðf0Þþ/S
¼p. The phase shift induced by head ﬁltering can be approxi-
mated by the time needed by the sound wave to travel around
the spherical head from its impact point with the head to the
right ear. This distance is called an “orthodromic”
and is the distance rOD(p
on a sphere of radius r(Deza and Deza, 2006), see Fig. 7and
Appendix Dfor details. We can therefore approximate the
phase difference /S
where D/Ris a propagation delay that does not depend on
frequency. This is applicable when the wavelength is small
compared to the head size. Thus our estimates of interfer-
ence parameters for a rigid surface with r¼1 are now
Table III shows that the interference spectral period f
very well approximated by this formula, while the ﬁrst inter-
ference frequency f
is overestimated. Part of the explanation
is probably the additional delays in low frequency intro-
duced by diffraction (Kuhn, 1977), which we did not take
into account in our formula.
3. Impact on ITDs and ILDs
As is shown in Fig. 8, these monaural interferences result in
oscillations in ILD and ITD as a function of frequency. When
the sound is reﬂected on a vertical wall [Figs. 8(A) and 8(B)],
the spectral period f
of interferences is different for the two
ears, which has two consequences. First, all spectral notches at
each ear are seen in the ILD. For instance, in the example shown
in Figs. 8(A) and 8(B) [aswellasFig.6(A)], because the wall
TABLE III. Computed values derived from Eq. (5) and prediction for the ﬁrst notch and the interference spectral period frequency [see Eq. (10)].
Wall reflection Ground reflection
Left ear Right ear Left ear Right ear
First notch Computed value r¼10
3357 Hz 1375 Hz 1011 Hz 1011 Hz
Computed value r¼610
4428 Hz 1871 Hz 1216 Hz 1179 Hz
Estimate (r¼1) 6105 Hz 2675 Hz 1352 Hz 1376 Hz
Spectral Period Computed value r¼10
10 240 Hz 4876 Hz 2626 Hz 2695 Hz
Computed value r¼610
11 378 Hz 5120 Hz 2695 Hz 2768 Hz
Estimate (r¼1) 12 211 Hz 5351 Hz 2703 Hz 2753 Hz
FIG. 7. The orthodromic distance OD between the point of incidence of a
source S with the surface of a sphere (incidence angles ðhS;uSÞ) and the ear
(coordinates ðhM;uMÞ). See Appendix Dfor the formulas.
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 15
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faces the left ear, the variations of acoustical pressure vs fre-
quency are stronger for the left ear. Thus, the ﬁrst maximum in
ILD [Fig. 8(A)] stems from the right ear (1871 Hz), though the
strongest one comes from the left ear (4428 Hz). The two inter-
ference spectral periods from each ear are present in the ILD in-
terference pattern—note the irregular oscillatory pattern in Fig.
8(A). Second, the interference patterns for both ILD and ITD
are much stronger for the wall reﬂection than for the ground
reﬂection. Indeed, for a reﬂection at the ground, the monaural in-
terference patterns are similar for the two ears, with almost iden-
tical values across ears for both f
(Table III). This is
because the direct and reﬂected sound have the same lateral
angle, so that /S
RðfÞ. As a consequence, the ILD is
much less affected than with a reﬂection at a wall.
With weakly reﬂective textures such as snow, interfer-
ences in ITDs and ILDs are not visible with a ground reﬂec-
tion. They are present, although reduced, with a wall
reﬂection. With strongly reﬂective textures such as asphalt,
the magnitude of interferences is larger compared to the r
values used here.
Monaural spectral notches correspond to dramatic
changes in ITD. For this reason, the same interference pat-
tern is expected in the ITD vs frequency curve as in the ILD
vs frequency curves. However, while the spectral periodicity
of these patterns agree well, the precise frequencies of
extrema in ITDs can be more difﬁcult to predict: for a reﬂec-
tion at the ground, monaural interferences are similar in both
ears and the abrupt changes in ITDs match the extrema in
ILDs [see Fig. 8(D)], but for a reﬂection at a wall, the de-
structive interferences may appear at different frequencies at
the two ears, and the resulting binaural interference pattern
is more complex. In general, the extrema in ITDs and ILDs
are interlaced, and extrema in ITDs are closer to extrema in
ILDs when the reﬂecting surface is harder. For instance, in
Fig. 8(B), the ﬁrst peak in ITD is almost in the middle of two
ILD extrema for r¼105(gray solid line) while it is close to
the ﬁrst peak in ILD for r¼6105(black solid line).
We may wonder whether these interference patterns
overlap with the hearing range of various species. In
Table IV, we report the computed values f0¼1=ð2ðDþ
D/RÞÞ as an estimate for the ﬁrst extrema in ILD=ITD after
ground reﬂection for the animals in Table I. The interference
spectral period fpwould be close to twice these values. This
estimate corresponds to an acoustically hard surface—
remember that the calculated values will be slightly lower
for an acoustically softer surface which introduces an addi-
tional delay in low frequencies. For these calculations, ear
position and head radius were estimated from photographs,
and for simplicity assuming a spherical head (many animals
do not have. This has only a limited inﬂuence on ﬁnal val-
ues). For tall mammals such as humans, Table IV shows that
ITDs and ILDs can be disturbed at low frequencies. How-
ever, it could be argued that the law of the ﬁrst wavefront,
which occurs for such delays, will limit this impact by sup-
pressing the reﬂection. We return to this issue in the discus-
sion. For small mammals (e.g., cats, gerbils, guinea pigs),
FIG. 8. Panels A and B show the ILD and ITD estimated from HRTFs of the sphere model after reﬂection by a wall. Panels C and D show these ILD and ITD
after reﬂection by the ground. The parameters of the source following the conventions of Fig. 1are indicated at the top. The parameters of wall- and ground-
reﬂected waves are shown within plots A and C, respectively.
16 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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the interference spectral period f
is generally large for sour-
ces at a polar angle of 0, unless they are very close, and
therefore only the ﬁrst extremum f
is expected to impact
sound localization. However, for a ﬁxed source at distance
1.5 m and height 1 m (two last rows), giving a high polar
angle for small mammals, both f
fall within the physi-
ologically relevant frequency range for these animals. In this
case, interferences in ITD and ILD may impact sound local-
ization. At ﬁrst sight, it would seem that this impact is nega-
tive because it degrades the “normal” binaural cues.
However, as is outlined in the next section, if these interfer-
ences can be systematically related to the source location, in
particular distance, then they may also provide a usable cue
for sound localization.
IV. INTERFERENCES AS LOCALIZATION CUES
The interference pattern is determined by the delay
between the direct and reﬂected sounds, which depends on
the location of the source. In Fig. 9, we show the computed
change in ILD and ITD produced by the reﬂection (see
Appendix E), as a function of frequency and either polar
angle or lateral angle, for a reﬂecting surface with a ﬂow re-
sistivity of 6 10
The interferences in the ITD vs frequency curves follow
the same pattern as in the ILD vs frequency curves. Similar
interference patterns as a function of polar angle have been
obtained from real recordings of ILDs in gerbils after reﬂec-
tion by a plywood ﬂoor (Maki et al., 2003). It can be seen
TABLE IV. Approximation of spectral period and ﬁrst extrema frequency of interferences in sound waves incoming at the right ear in a ground reﬂection
model for the various species of Table I. The distance from the source is assumed to be 1.5 m and the same two sets of source height=polar angle as in Table I
are used. The lateral angle is assumed to be 40.
(Bulldog) Cat Gerbil
Head radius (cm) 8.75 8 9 4.5 1.3 2 0.8
Angles hM;uM() 100,5 110,30 110,30 110,40 110,40 110,30 110,40
(Hz) (across all sources considered in Sec. V, Fig. 12) 49 111 208 417 685 1042 4167
dist.: 1.5 m elev.: 0(source
height ¼ear-ground distance)
First extremum f
(Hz) 76 260 761 2831 8352 17 700 253 000
Interference period f
(Hz) 152 520 1522 5662 16 700 35 400 506 000
dist.: 1.5 m source height ¼1m
First extremum f
(Hz) 107 205 342 659 1182 1685 6045
Interference period f
(Hz) 214 410 684 1318 2364 3370 12 000
FIG. 9. The ITD and ILD changes produced by a reﬂection (A,B: ground; C,D: wall). In panels A and B, the lateral angle is set to 40for the ground reﬂec-
tion, as in Fig. 8. In panels C and D, the polar angle is set to 40for the wall reﬂection.
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 17
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that there is a systematic variation in both the ﬁrst interfer-
ence frequency f
and the interference spectral period f
polar angle for ground reﬂection and lateral angle for wall
reﬂections. These two values might thus be usable as local-
ization cues. However, for a reﬂection at a wall, they also
depend on the location and orientation of the reﬂecting sur-
face, which are very variable in real environments (see
Appendix B). The unpredictable variability in binaural cues
may therefore be seen as “noise” but for a reﬂection at the
ground, this variability is predictable, because the ground is
generally approximately horizontal and at a ﬁxed distance
from the ears. Indeed, if the polar angle is known, then the
distance from the source can be estimated from the ﬁrst in-
terference frequency f
or the interference spectral period f
[Fig. 10(A)]. As we have seen, these two values are not very
sensitive to the nature of the ground. Conversely, if the dis-
tance is known, then the source polar angle can be estimated
[Fig. 10(B)]. Nevertheless, the interference spectral period
would probably not be a very helpful localization cue for
large distances, because very few interference peaks occur
within the physiological frequency region, as the second
peak occurs at frequency f
. However, the ﬁrst in-
terference frequency would remain useful over a larger dis-
It is also useful to look at the change of the values of
ITD and ILD relative to when there is no reﬂection. In
Fig. 11, we show this relative change for the situation shown
in Figs. 6and 8. It appears that ILD is more affected than
ITD, both for ground and wall reﬂections. Even for the mod-
erate ﬂow resistivity value rof 6 10
used for the calcula-
tions in this ﬁgure, the variations in ILDs are very large in
both cases, especially for low frequencies. Indeed, many
surfaces are very reﬂecting in low frequency and the ILD is
very small in the absence of reﬂections. Both binaural cues
are much less affected by the ground than by the wall.
Although the position of the ITD and ILD extrema depends
on the delay between the direct and reﬂected sounds and
thus may be viewed as information, the amplitude of the
changes depends on surface type: the amplitude is higher for
more rigid surfaces. In general, then, these may be seen as
FIG. 10. Panel A shows, for the ground reﬂection, the relationship between source-head distance (vertical axis) and interference pattern spacing and ﬁrst
extrema (horizontal axis), for a polar angle of 0. Panel B shows, for the ground reﬂection, the relationship between polar angle and interference pattern spac-
ing and ﬁrst extrema, for a source-head distance of 1.5 m. The source is assumed to be at the same level as the animal and its lateral angle is 40.
FIG. 11. The relative change in ITD and ILD due to reﬂections, compared to ITD and ILD of the direct wave, for the source parameters used in Figs. 6and
10. The sound wave is reﬂected by (A) the ground or (B) a wall. The ﬂow resistivity is r¼610
18 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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degradation of binaural cues, and it appears that ITD is the
V. RANGES OF ITD AND ILD WITH REFLECTIONS
We now look at how reﬂections change the range of
ITDs and ILDs processed by the auditory system. We calcu-
lated the maximum ITD and ILD as a function of frequency
across lateral angle and polar angle coordinates within a
large grid of 393 spherical positions evenly distributed
around the sphere (between –45and 90polar angle), simi-
lar to that in Behrend et al. (2004), and for distances between
1 and 20 m at increments of 50 cm. Figure 12 shows the
results for ground and wall reﬂections. In both cases, the
range of ILDs is greatly extended, especially in low frequen-
cies where ILDs are usually small. Without reﬂections, ILDs
are always smaller than about 10 dB. With a reﬂection at a
wall, they can reach more than 30 dB. This phenomenon is
accentuated by surfaces with higher ﬂow resistivities.
The range of ITDs is not strongly affected by a reﬂec-
tion at the ground, but it is very much extended with wall
reﬂections, as was noted by McFadden (1973). Without
reﬂections, the ITD changes continuously with frequency
and therefore it is usually estimated by “unwrapping” the
IPD, that is, by considering that ITD is a function of fre-
quency that is consistent with IPD modulo 2pand has mini-
mum variation: j2pf2ITDðf2Þ2pf1ITDðf1Þj <pfor two
neighboring frequencies f
. This does not work with
reﬂections because destructive interferences make ITD a
discontinuous function of frequency. Therefore, for Fig. 12,
we chose a conservative estimate, by choosing the ITD con-
sistent with IPD that is closest to the anechoic ITD (see
details in Appendix E). Thus the range of ITDs with reﬂec-
tions shown in Fig. 12 is an underestimation. For high fre-
quencies, this underestimation is not very informative
because the method artiﬁcially constrains the estimate to be
within 1=(2f) of the anechoic ITD. This is known as the
p-limit (Brand et al., 2002;Hancock and Delgutte, 2004;
Joris and Yin, 2007;McAlpine et al., 2001). However, for
low frequencies and reﬂections on a wall, ITDs can be arbi-
trarily large within this limit, especially for surfaces with
high ﬂow resistivities. Indeed, as we have seen, the IPD is
close to pnear a destructive interference. This means that
the range of ITDs is very much extended by reﬂections at
low frequencies compared to an anechoic environment.
VI. DISCUSSION AND SUMMARY
A. Limitations of the models
Although we have tried to consider realistic acoustic
properties for the reﬂecting surfaces, our models rely on a
number of approximations.
First, we did not consider the frequency-dependent
absorption properties of air (ISO 9613-1:1993, 1993). In par-
ticular, high frequencies tend to be more attenuated than
lower frequencies and the effect depends on distance. How-
ever, as we only considered early reﬂections, the spectrum
of the direct and reﬂected sounds should be almost identical,
FIG. 12. The panels A and B show the maximum ILD and ITD with and without ground reﬂections, for sounds between 1 and 20 m from the head and with a
ground-head distance of 0.08 m. The panels C and D show these maximum ILD and ITD with and without wall reﬂections. The p-limit and the ITD corre-
sponding to the distance between the two ears (3.8 cm in the sphere model) are indicated in dashed lines in B and D.
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 19
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and therefore the differential effects of air absorption should
Second, we only considered a single reﬂection. In a real
environment, there are many more reﬂections. In addition,
under speciﬁc atmospheric conditions, a downward refraction
by the atmosphere might generate additional ray paths and
therefore one or more reﬂections to the ground (Sutherland
and Daigle, 1998). Late reﬂections are assumed to be sup-
pressed by the auditory system, via the precedence effect, but
there may be additional early reﬂections. However, at least
for low frequencies, most of the reﬂected power should be
contributed by large ﬂat and thick surfaces such as the ground.
But a natural ground is not a perfectly horizontal surface. In
particular, small irregularities such as rock or stones may
heavily deviate and attenuate the reﬂection of high frequency
sounds. For instance, an obstacle of less than 5 cm interferes
with sound waves above 7 kHz. As a consequence, interfer-
ences at such high frequencies might be of lower amplitude in
real environments than in our model. We also assumed that
the texture is homogeneous and of inﬁnite depth, which is
clearly not the case in natural environments. Nonetheless,
many studies have shown that ﬁeld measurements of sound
propagation are in close agreement with the theoretical mod-
els used in this paper, in particular for grass which has an av-
erage ﬂow resistivity similar to the values we used (Chessell,
1977;Embleton et al., 1983;Rasmussen, 1981).
Thirdly, the sphere is a highly simpliﬁed model of the
head of an animal. We introduced shifted ears but other
aspects such as the nose and the torso also play a role in the
diffraction of sounds by the body.
Finally, we only considered point sources with omnidir-
ectional directivity (i.e., monopoles). Real sources may devi-
ate from this model, for example human speech or mammal
vocalizations are not omnidirectional. For these sources, we
would expect that the direct sound has more power than the
B. Impact of reflections on binaural cues
For many small animals such as cats and guinea pigs,
the ground contributes early reﬂections with delays no lon-
ger than about a millisecond. This maximum delay is only
for a sound source near the ears and it quickly decreases
with distance: for example, it is just 150 ls for a sound
source at 1.5 m from the head of a cat. It is unlikely that
such reﬂections can be suppressed by the auditory system,
considering that psychophysical measurements indicate that
the threshold for fusion is close to 1 ms. Therefore, the
reﬂection modiﬁes the binaural cues perceived by the ani-
mal, and so the perceived binaural cues in an ecological
environment, even a simple one with only a ground, are not
the same as in an anechoic environment.
In barn owls, a number of studies have addressed the
neural and behavioral correlates of acoustical reﬂections
(Keller and Takahashi, 1996a,1996b,2005;Nelson and
Takahashi, 2010;Spitzer and Takahashi, 2006). In a natural
environment, the ground can be far from the owl’s ears when
it ﬂies, but when it is about to catch its prey the ground is
very close. Therefore the same remarks as for small animals
apply, and the maximum delay of the reﬂected sound is a
fraction of millisecond. For example, for a mouse just below
the owl, the delay is about 100 ls, which corresponds to an
interference at frequency 5 kHz, right in the middle of the
hearing range of these animals. This is well below the fusion
threshold for owls, about 0.5 ms (Keller and Takahashi,
1996a,1996b). In binaural neurons of the inferior colliculus,
the response to a reﬂection is suppressed when the delay is
longer than 0.5 ms, but it is consistent with cross-correlation
of the summed direct and reﬂected signals below 0.5 ms
(Keller and Takahashi, 1996b). This suggests that the
reﬂected signal is indeed retained by the auditory system for
such short delays. These electrophysiological observations
are consistent with behavioral measurements, in which owls
turn their head to the leading sound when the delay is longer
than 1 ms (Keller and Takahashi, 1996a).
The combination of the direct and reﬂected sounds
leads to monaural interferences, around frequencies
f¼1=(2D)þn=D, which are then seen in binaural cues. Peri-
odic distortions in ILDs have been previously reported in
studies of simulated gerbil HRTFs with ground reﬂection
(Grace et al., 2008) and in human HRTFs with ground reﬂec-
tion (Rakerd and Hartmann, 1985) or for the ear facing a very
near wall (Shinn-Cunningham et al.,2005). The largest modi-
ﬁcations occur for reﬂections at a vertical wall, because the
lateral angle and therefore the binaural cues are very different
for the two sounds. For a reﬂection at the ground, the modiﬁ-
cations are smaller but still very signiﬁcant near interference
frequencies. ILDs are typically more affected than ITDs,
because ILDs are deﬁned as a ratio of monaural levels.
Indeed, even though a constructive interference cannot pro-
duce a gain larger than 6 dB, the change in ILD can reach
10–15 dB because of destructive interferences.
C. Humans vs small animals
We have focused our study on small animals that live on
the ground. In these animals, delays between direct and
reﬂected sounds are very short in many situations. For
humans, the delays of reﬂected sounds can be longer, up to
10 ms for a reﬂection at the ground. It might be argued that
this is beyond the fusion threshold and therefore such echoes
should be suppressed by the auditory system. However, there
are reasons to think that our results may also apply to
humans. First, the delays are shorter when the source is far
[the delay is <1 ms when the source is >15 m away, see
Fig. 3(A)], and therefore interferences in binaural cues
should be seen for distant sources. Second, even when the
delay is long, the processing of binaural cues by the auditory
system might still be impacted, because they are processed
in frequency bands, where the direct and reﬂected sounds
may interact. The duration of the impulse response of an au-
ditory ﬁlter is inversely related to its bandwidth and there-
fore with its center frequency, and two delayed impulse
responses interact if the delay is shorter than a few periods.
The ﬁrst interference occurs at frequency f¼1=(2D): for
that frequency, the delay corresponds to only half a period of
the waveform. Therefore, this interference should be seen in
the response of binaural neurons, at least in the earliest
20 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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stages of the binaural pathway. This means that, in the
responses of these neurons, the direct and reﬂected sounds
should merge when the delay is smaller than a value which
is inversely proportional to frequency. This is consistent
with psychophysical measurements in humans (Dizon and
Colburn, 2006;Kirikae et al., 1971).
Thus it seems plausible that early reﬂections also inter-
fere with direct sounds in humans and affect binaural cues, so
that all the results shown here should also apply to humans.
The main difference with small animals is that humans stand,
and therefore the ground is further from the ears. This implies
that delays between direct and ground reﬂected sounds are
typically longer for sources in the horizontal plane, even at
relatively far distances. Longer delays mean lower interfer-
ence frequencies. For example, with a 10 ms delay, the ﬁrst
interference frequency is 50 Hz and the next ones are at 150
and 250 Hz; with a 6.5 ms delay, i.e., a distance of 1.5 m,
they are 77, 231, and 385 Hz. These are in the hearing range
of humans. In addition, as we have seen in Sec. III B, natural
surfaces are generally very reﬂecting at low frequencies.
Moreover, humans typically stand on artiﬁcial textures such
as concrete or asphalt that are strongly reﬂective. Therefore,
we expect strong modiﬁcations of low frequency binaural
cues for sources at the same height as the listener. Finally, we
note that, as for owls, the delays are short if the source,
instead of the ears of the listener, is close to the ground. In
this case, all the results we have shown directly apply.
D. Noise and information contributed by early
The interferences between direct and reﬂected sounds
modify the binaural cues, especially ILDs. These modiﬁca-
tions could be seen as a source of noise in the localization of
sound sources. The relevant issue is the variability of these
cues for a given location, when other unknown factors are
allowed to vary, for example the nature of the ground or the
exact orientation of the reﬂecting surface. With this point of
view, the changes introduced by walls or similar obstacles
would qualify as noise, because they are large and very sen-
sitive to other parameters that seem difﬁcult to precisely esti-
mate by other means, such as the orientation and texture of
the obstacle. Indeed, performance in localization is degraded
by strong reﬂections (Croghan and Grantham, 2010;Gigue`re
and Abel, 1993;Rakerd and Hartmann, 2005) and vision is
given a stronger perceptual weight (Truax, 1999).
How can the auditory system deal with these disturban-
ces? For broadband sounds, frequency integration might be a
useful strategy: ITDs and ILDs vary with respect to frequency
around an average value which could be used to estimate the
source location, as seen in Fig. 8. In echoic environments,
human performance is indeed poor for pure tones (Hartmann,
1983;Rakerd and Hartmann, 1985) and transients seem to be
important for localization in rooms (Hartmann and Rakerd,
1989;Rakerd and Hartmann, 1985). Another possible strategy
for continuous sounds is to use the motion of the source or the
voluntary motion of the head, and to select the most favorable
conﬁgurations—for example, on the basis of variability of
binaural cues across frequency. However, we note that the
detectability of a masked signal is not generally improved by
its motion (Xiao and Grantham, 1997). A third hypothesis is
that the auditory system may select the most “plausible” bin-
aural cue: for example, very large values for ITDs could be
seen as implausible and discarded, giving a stronger weight
for ILD (Rakerd and Hartmann, 1985). We found that ITDs
were generally less affected by reﬂections than ILDs. This
would suggest that the auditory system should rely more on
ITDs than on ILDs. However, for high frequencies, ITD is
ambiguous unless the sound is broadband. Even though high
frequency neurons in the inferior colliculus are sensitive to
envelope ITDs (Grifﬁn et al.,2005;Joris, 2003;Nelson and
Takahashi, 2010), a recent study of the directional sensitivity
of such neurons in reverberation suggests that ILD provides
better directional information than envelope ITDs in high fre-
quencies (Devore and Delgutte, 2010).
Binaural cues are less affected by reﬂections at a ground
than at a wall, especially ITDs. More importantly, even
though binaural cues differ from the anechoic case, they are
not very variable: the ground is generally horizontal, the dis-
tance between the ears and the ground is ﬁxed (or at least
likely to be known by the animal) and the inﬂuence of the na-
ture of the ground is relatively small. As we have seen, the in-
terference frequencies are directly related to the delay
between the direct and reﬂected sounds, and therefore to the
polar angle and distance. The amplitude of these interferences
depends on the nature of the ground, but their frequency does
not. Therefore, interferences contributed by the reﬂection at
the ground are a potential spatial cue. It is known that rever-
beration contributes to the perception of distance and spa-
ciousness (e.g., Blauert, 1997;Truax, 1999)—in particular,
the reverberation time. However, the role of single reﬂections
has not been fully described. Preliminary results show that
spatial maps of some neurons are unexpectedly more accurate
with a reﬂection than in free-ﬁeld, at least in the external
nuclei of the inferior colliculus of the gerbil (Maki et al.,
2005). We suggest that interferences in binaural cues might
provide a cue to distance and=or polar angle.
The main cues for polar angle are thought to be (1) mon-
aural spectral notches introduced by the direction-speciﬁc
attenuation of particular frequencies by the pinna (Algazi
et al., 2001;Blauert, 1997;Musicant and Butler, 1985;
Tollin and Yin, 2003;Wightman and Kistler, 1992) and (2)
head movements (Blauert, 1997;Thurlow et al., 1967).
Spectral notches occur at high frequencies and their fre-
quency is positively correlated with polar angle (Maki and
Furukawa, 2005;Tollin and Yin, 2003) while the inverse
correlation is seen for the interference frequencies [see Fig.
10(B)]. Therefore, these two cues to polar angle should be
essentially independent. The potential role of interferences
in polar angle estimation was noticed in a similar study on
simulated HRTFs of gerbils with ground reﬂection (Grace
et al., 2008), and is also in agreement with a psychoacousti-
cal study showing that the polar angle of the sound source
was estimated with greater accuracy with a sound-reﬂecting
surface on the ﬂoor (Guski, 1990). This effect was not seen
with a wall reﬂection, which suggests that the auditory sys-
tem indeed relies on the knowledge of the head-ground dis-
tance to extract the relevant information.
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 21
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However, interference frequency provides an ambiguous
cue to polar angle because it also depends on distance. Dis-
tance perception is generally seen as less accurate than for
lateral angle and polar angle in mammals (Bronkhorst and
Houtgast, 1999;Zahorik et al.,2005). Several cues have been
previously investigated [see reviews in Coleman (1963),Mer-
shon and Bowers (1979) and Brown and May (2005)]: (1)
level of known sounds: the sound intensity varies with dis-
tance according to the inverse-square law; (2) frequency
spectrum: high-frequency components of broadband signals
are attenuated more rapidly by air propagation than low-
frequency ones; (3) movement parallax: the direction of a
source is less modiﬁed by listener movements for a distant
source than for a close source; (4) acoustic ﬁeld width: it
should be larger for a close source; (5) direct-to-reverberant
energy ratio: at long distance, the many reﬂections induced
by the propagation of sounds in all directions increase the
amount of energy received after the direct sound wave
(Bronkhorst and Houtgast, 1999;Mershon and King, 1975;
Shinn-Cunningham et al.,2001;Yan-Chen Lu and Cooke,
2010;Zahorik et al., 2005). Many studies on distance percep-
tion suggest that auditory image distortion, including reﬂec-
tions and scattering, by natural environments is an important
cue for distance perception (Brown and Gomez, 1992;Brown
and Waser, 1988;Waser and Brown, 1986;Wiley and Rich-
ards, 1978). For instance, it has been shown that distance
judgments are more accurate in a reverberant space than in an
anechoic space (Mershon and Bowers, 1979;Mershon and
King, 1975;Nielsen, 1993;Sheeline, 1982;Zahorik, 2002).
In addition to these cues, our results suggest that binaural
interferences might be another one. Nevertheless, for sources
in the horizontal plane, which is probably the most common
situation, interferences occur at high frequencies (>20 kHz)
at distances greather than 2 m for guinea pigs [Fig. 10(A)],
meaning that only a few interference peaks will fall within
the hearing range of the animal. For these species, this cue
might therefore be more useful for close sources. For humans,
these interferences could provide information over a larger
range (for example, the ﬁrst interference frequency is 76 Hz
at 1.5 m, see Table IV). This hypothesis could be tested with
These interferences are also seen in monaural signals,
and therefore they could be seen as monaural cues. However,
only the binaural cues are independent of the sound source:
for example, frequency-dependent changes in level in a mon-
aural signal can be due either to reﬂections or to the spec-
trum of the source. If binaural rather than monaural
interference cues are used by the auditory system, one pre-
diction is that their effect should only be seen away from the
median plane, where ITDs and ILDs are essentially zero.
Whether early reﬂections come from the ground or from
a wall, and even though their impact on binaural cues may
depend on many factors, these binaural cues are reproducible
and temporally stable. Thus, even if ITDs and ILDs cannot
be unambiguously mapped to the location of the sound
source, they could still be used as reliable spatial cues to iso-
late a sound source from a noisy background. Perhaps a per-
son or animal could learn to associate a source with a
particular pattern of frequency-dependent ITD and ILD,
which could then be used to isolate its signal from those of
competing sources, even if this binaural pattern cannot be
accurately associated with a particular spatial location. This
suggestion has an important implication: the large ITDs and
ILDs due to early reﬂections are not simply “noise” to be ﬁl-
tered, but instead are naturally occurring cues that may be
encoded by the auditory system.
E. The natural distribution of binaural cues
When early reﬂections are considered, the range of ITDs
and ILDs is extended, compared to the anechoic case. This
observation is most interesting for ITDs. In an anechoic envi-
ronment, the ITD is limited by the size of the head. For exam-
ple, in humans, it does not exceed 650–700 ls in high
frequencies. In low frequencies, it can be about 50% larger
because of diffraction effects (Kuhn, 1977), but it is still lim-
ited. However, with an early reﬂection, we have seen that a
discontinuity in IPD occurs at the interference frequency, and
this implies that the IPD can be arbitrarily large. This means
that the ITD can take any value within the p-limit, i.e.,
between 1=(2f)and1=(2f), where fis the frequency. In
many species, many binaural neurons are tuned to best delays
that are greater than the maximum range of ITDs in an
anechoic environment (McFadden, 1973). The proportion of
such neurons differ between species but it has been consis-
tently observed in rabbit (Kuwada et al., 1987), guinea pig
(McAlpine et al.,2001), cat (Hancock and Delgutte, 2004;
Kuwada and Yin, 1983;Yin and Chan, 1990), gerbil (Brand
et al.,2002), chinchilla (Thornton et al., 2009), kangaroo rat
(Crow et al.,1978), chicken (Ko¨ppl and Carr, 2008), and
barn owl (Wagner et al.,2007). In most of these studies, this
proportion is overestimated because the best delays are com-
pared to the maximum ITD measured in high frequencies,
which is smaller than the actual range incorporating the dif-
fraction effects in low frequency (compare for example
McAlpine, 2005 and Sterbing et al.,2003). However, it
remains that a signiﬁcant number of binaural neurons are
tuned to ITDs that lie outside the range of anechoic ITDs.
This observation has motivated a new theory of ITD process-
ing in mammals, according to which ITD is represented by
the relative activity of two populations with symmetrical best
delays lying outside the natural range (Grothe et al., 2010), a
strategy sometimes referred to as slope coding or the two-
channel model. This theory is in contrast with the “peak
coding” theory (Carr and Konishi, 1990), where ITD is repre-
sented by the best delay of the maximally activated neuron.
Note that other coding strategies are possible (Colburn,
1973). Our results imply that the natural range of ITDs is
much larger than expected from anechoic measurements
when considering reﬂections on the ground or on obstacles: it
can take any value within the p-limit. Therefore, the large
best delays observed in binaural neurons of small mammals
are consistent with peak coding, and more importantly they
make the two-channel model problematic because the ratio of
activities in the two channels is an ambiguous representation
of ITD when the best delay lies within the natural range of
ITDs, i.e., different ITDs give the same ratio. It could be
argued that large ITDs due to reﬂections are disturbances and
22 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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therefore there is no reason for the auditory system to encode
them. However, as we have seen, for a reﬂection at the
ground, these large ITDs due to reﬂections contribute infor-
mation about sound location rather than noise, because they
are reproducible cues. For reﬂections on walls or obstacles,
even though these ITDs may not contribute information about
sound location, they are still temporally stable and therefore
potentially convey spatial information for segregating sound
sources. Thus, it does not seem implausible that the auditory
system may encode these large ITDs.
In addition, we also note that binaural neurons compare
the information only after the physical signals have been
processed by the auditory periphery. As has been noted by
other authors, such nonlinear processes, including for
instance half-wave rectiﬁcation and adaptation, can cause
monaural interactions between direct and reﬂected sounds
that can result in unexpected changes in the cues effectively
seen by the binaural neurons (Hartung and Trahiotis, 2001;
Trahiotis and Hartung, 2002).
In realistic auditory environments, binaural cues can be
modiﬁed by reﬂections. When the delay between the direct and
reﬂected sounds is long, the auditory system can isolate the
onset of the direct sound. However, in many cases, these delays
are very short. For example, for a reﬂection at the ground, the
delay of the reﬂected sound is no more than 2p=c,wherepis
the distance of the ears from the ground and cis the speed of
sound. This gives about 10 ms for humans, about 1 ms for cats
and less for smaller mammals. In many practical situations, the
delay is substantially lower than this higher limit.
This delay Dresults in destructive interferences at
each ear at frequencies about f¼1=(2D)þn=D,wherenis
an integer, which produce large modiﬁcations of ITDs and
ILDs near these frequencies. Therefore, binaural cues in an
ecological environment, even a simple one with only a
ground, are not the same as in an anechoic environment.
These modiﬁcations are larger for ILDs than for ITDs.
They are larger for a vertical wall than for a horizontal
ground, because the interaural axis is parallel to the
ground. In all cases, they remain very signiﬁcant near inter-
ference frequencies. These modiﬁcations depend on the
delay of the reﬂected sound, and therefore on source dis-
tance. At a ﬁner level of detail, they also depend on the
acoustical properties of the reﬂecting surface. Hard surfa-
ces (e.g., concrete) reﬂect more energy than soft ones (e.g.,
snow) and therefore have a stronger impact on binaural
cues, but the impact is signiﬁcant with typical natural
surfaces. The analyses also imply that the range of ITDs
and ILDs in natural environments is signiﬁcantly extended
compared to the anechoic case.
As a ﬁnal remark, we note that the ears of small mam-
mals are very close to the ground and possibly to objects on
the ground, making their acoustical environment more vari-
able. Thus, their acoustical cues for sound localization may
be quite different from those available to humans, with their
ears about 1.70 m above the ground. These differences
should be kept in mind when extrapolating the results of
animal studies to humans, or to other species: binaural cues
do not only depend on the shape of the head and ears, but
also on the properties of the natural acoustical environment.
This work was supported by the European Research
Council (Grant No. ERC StG 240132). We thank the
reviewers for their constructive suggestions. We also thank
Marc Re´billat for comments on the manuscript.
APPENDIX A: LIST OF SYMBOLS
uSIncidence angle of the reﬂected wave on the wall
arg Argument of a complex number
cSpeed of sound (343 m=s here)
dDistance source-ears (direct path)
d* Distance source-ears (reﬂection path)
dAbsolute delay of the direct sound
d* Absolute delay of the reﬂected sound
DDelay direct sound—reﬂection (airhead model)
D at the left=right ear, respectively
D/RDelay at the right ear between direct and reﬂected waves due to
sound diffraction (s)
erfc Complementary error function
First notch frequency in a spectrum (Hz)
Interference pattern spacing in a spectrum (Hz)
Polar angle for the left ear
Polar angle of a point source S
F“Ground wave” function
HHead related transfer function (HRTF)
HRTF after reﬂection
HRTF at the left=right ear, respectively
hmm-th order spherical Hankel function
iImaginary number: square root of 1
kiWave numbers of the sound ﬁeld in the i-th media
OCenter of the head
OD Orthodromic distance
pDistance head-ground or head-wall)
Complex pressure at the receiver
m-th order Legendre polynomial
QSpherical reﬂection factor
rRadius of sphere
RPlane wave reﬂection coefﬁcient
qNormalized distance to the source
r“Effective” ﬂow resistivity (Pa.s.m-2)
Signal at the left=right ear, respectively
sPhase delay of Q
Lateral angle for the left ear
Lateral angle of a point source S
(X,Y,Z) Cartesian coordinate system
Cartesian coordinates of S
ZiSpeciﬁc acoustic impedances of the i-th media
J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´vitch and R. Brette: Impact of early reflections 23
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APPENDIX B: GEOMETRICAL MODELS OF
We consider the case where a sound wave is reﬂected at
an obstacle before reaching its target. We consider two situa-
tions: reﬂections on a horizontal ground or on a vertical
wall, parallel to the median plane (Fig. 2). We give here the
detailed calculations for the delay between direct and
reﬂected sounds as a function of the distance from the source
to the head and the polar (ground case) or lateral (wall case)
angle of the sound source to the head. Following the notation
used in Fig. 2, the angles of the reﬂection relative to the head
are given by the following equations, in the case of a reﬂect-
In the case of a reﬂecting wall, both lateral and polar angles
are modiﬁed by the reﬂection. The easiest way to compute
angles for S* is to consider the Cartesian coordinates system
(X,Y,Z): in that, S* is a translation of Salong the Yaxis (that
of the two ears, which is perpendicular to the wall and there-
fore parallel to SS*). We have
These results are used in the geometrical models of reﬂec-
tions described in Sec. II.
APPENDIX C: ACOUSTICAL MODEL OF
REFLECTIONS ON NATURAL SURFACES
Here, we give details of a model for the modiﬁcations of
a sound wave when it is reﬂected by a natural surface in a re-
alistic outdoor environment. In the following, we describe
the ground-reﬂection model. The equations are identical for
the wall-reﬂection model, with uSreplaced by the incidence
of the reﬂected wave on the wall. Note that as the
wall being parallel to the (X,Z) median plane (see Appendix B),
then if Ois the center of the head, a
is equal to the angle
between OS* and its projection on the median plane (X,Z).
As explained in Sec. II B, we use the Weyl–Van der Pol so-
lution (Sutherland and Daigle, 1998) for the boundary condi-
tions of a spherical sound wave reﬂected on a plane. The
complex sound ﬁeld P
at the receiver is well approximated
by the equation
where Qis the spherical reﬂection factor and P(d,f) is the
sound ﬁeld amplitude at frequency fand distance dfrom the
source in the absence of reﬂecting surfaces. In the following,
all quantities except angles implicitly depend on frequency.
Qcan be written as Q¼Rþ(1 R)F(w), where Ris the
plane wave reﬂection factor and ð1RÞFðwÞis a boundary
correction. The plane wave reﬂection coefﬁcient Ris (Ches-
sell, 1977;Embleton et al., 1983)
Z1and Z2are the speciﬁc acoustic impedances of the air and
ground surface, respectively. FðwÞ, also known as the
“ground wave” function or as the “boundary loss factor,” is
is called the “numerical distance,” erfc is the complementary
error function, k1and k2are the wave numbers of the sound
ﬁeld in the air and ground surface, respectively. FðwÞ
describes the interaction of the curved wavefront with a
ground of ﬁnite impedance. If the wavefront is plane
(d!1) then jwj!1and F!0 while if the surface is
acoustically hard, then jwj!0 and F!1 (also R¼1), so
Q¼1. Numerical computation of Fis unstable for high val-
ues of wand was performed using algorithms in (Weideman,
The acoustic impedance of a surface (such as Z1and Z2)
is the ratio of the amplitude of the sound pressure to the am-
plitude of the particle velocity of an acoustic wave that
impinges on the surface. Both concrete and densely packed
24 J. Acoust. Soc. Am., Vol. 132, No. 1, July 2012 B. Goure´ vitch and R. Brette: Impact of early reflections
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glass ﬁber are high impedance materials relative to air,
whereas grass and some foams are low impedance surfaces.
If a sound wave changes medium, the ratio of the acoustic
impedances of the media Z2=Z1determines the efﬁciency of
the energy transfer.
There have been numerous models estimating k2=k1and
Z2=Z1for typical outdoor surfaces. A widely used one, called
the Delany–Bazley model (Delany and Bazley, 1970),
involves a single parameter, the “effective” ﬂow resistivity r
to characterize the ground. Its units are Pa s m
time conventions in Embleton et al. (1983) and improve-
ments of the Delany–Bazley model by Miki (1990) we have
which were considered valid in the range 0:01 <f
nally but which remain well behaved in a larger frequency
range. This model may be used for a locally reacting ground
as well as an extended reaction surface.
Several tables for ﬂow resistivity rhave been published
(see Cox and D’Antonio, 2009). They agree on values
around r¼2:104for snow, r¼105for grass ﬁelds or forest
ﬂoor, and around r¼6:105for sand or dirt, a roadside with
rocks less than 4 in. in size. rcan reach as much as 3 10
for asphalt or 2 10
for concrete. In this paper, we chose
r¼105and r¼6105as moderate values for rin order
to simulate credible outdoor environments encountered by
APPENDIX D: SPHERE MODEL
We describe here our model of HRTFs. We use a spheri-
cal head model with shifted ears, for which the diffraction
function is completely known and has been extensively
described, for instance, in (Duda and Martens, 1998;Ono
et al., 2008). Brieﬂy, simulated HRTFs can be obtained from
the frequency-domain solution for the diffraction of an
acoustic wave by a rigid sphere modeling the head.
The source Sis at a distance dfrom a sphere of radius r.
Let hbe the angle of incidence between the ray from the center
of the sphere to the source and the ray to the measurement point
on the surface of the sphere. Given the symmetry axis of a
sphere, one angle is enough to deﬁne the incidence angle. The
transfer function at the surface of the sphere is then given by
where q¼d=r1;l¼ð2pr=cÞf;hmis the m-th-order spher-
ical Hankel function, h0
mits derivative, and P
is the m-th order
Legendre polynomial (Rabinowitz et al., 1993;Rayleigh and
For a spherical head model, rhis equal to the shortest
distance that the sound wave has to cover to reach the ear,
i.e., the shortest distance at the surface of the sphere between
an ear of coordinates ðhM;uMÞand the incidence angles
ðhS;uSÞof the sound wave. This is equal to the orthodromic
distance rODððhS;uSÞ;ðhM;uMÞÞ between these two
points (see Fig. 7) given by Deza and Deza (2006):
(note that when ears are assumed to be antipodal,
i.e., ðhM;uMÞ¼ð90;0Þ, then ODððhS;uSÞ;ð90;0ÞÞ
¼arccosðcosuSsinhSÞ). Thus, the HRTF at the left ear can
be written HLðd;f;ODððhS;uSÞ;ðhM;uMÞÞ;rÞand that of
the right ear is HRðd;f;ODððhS;uSÞ;ðhM;uMÞÞ;rÞwith
the previous notations, assuming that ears are symmetrical
relative to the medial plane.
For computations made over all spherical positions, a
grid of 393 spherical positions evenly distributed around the
sphere (between –45 and 90polar angle) was used and is
the same as that found in Behrend et al. (2004).
APPENDIX E: ITD AND ILD ESTIMATES
The interaural transfer function (ITF) is typically
deﬁned as the ratio of contralateral and ipsilateral HRTFs,
which we will adapt here to the ratio of left and right HRTFs
for clarity of equations all over the paper since the wall is
placed on the side of the left ear, i.e.,
ITFðf;d;ðhS;uSÞÞ ¼ HLðf;d;ðhS;uSÞÞ
From the ITF, we derive the ILD and interaural phase differ-
ence (IPD) as follows:
ILDðf;d;ðhS;uSÞÞ ¼ 20 log10jITFðf;d;ðhS;uSÞÞj;(E2)
(where the ILD is in dB). To estimate the ITD of direct and
reﬂected sound waves, we chose a conservative estimate, by
choosing the ITD consistent with IPD that is closest to the
We thank Michael Akeroyd for his remark about the ellipsoidal locus of
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