Signal Processing - May 2017 - 40

undesirable effect can be partly alleviated by adding simulated
reflections and artificial reverberation.
Binaural audio can also be presented via a pair of loudspeakers; however, each ear then receives not only its intended signal
but also the signal intended for the other ear, which impairs the
coherence of binaural cues. This effect is known as crosstalk
[22]. There are methods for crosstalk cancelation based on predicting the response of the crosstalk path and inverting it [23].
Such methods preprocess the left and right channels using a
2 × 2 crosstalk cancelation filter matrix, which is obtained as the
inverse of the matrix containing the direct and crosstalk acoustic transfer paths. When a listener is sitting still at the position
for which crosstalk cancelation is made, a single set of crosstalk
cancelation filters can be very effective. However even small
head movements require filter adaptation, which increases the
computational overhead associated with crosstalk cancelation.
Crosstalk-canceled binaural audio, also known as transaural audio, has distinct benefits in comparison with two-channel
stereophony and headphone-based binaural presentation: 1) it
can simulate sources behind the listener, even when there is no

ICLD (dB) = 20 log10(gL/gR)
ICLD (ms) = dR -dL
Input

Delay dL

Stereophonic
Image

Delay dR

Gain gL

Gain gR

(a)

Auditory Event
Perceived at Right
Loudspeaker

16
12
ICLD (dB)

4 CL
0

-4
-8

1
1.
2

0.
8

0.
6

0.
4

0
0.
2

-1
.2
-1
.0
-0
.8
-0
.6
-0
.4
-0
.2

FL
-12 Auditory
-16 Event Perceived
at Left Loudspeaker
-20

ICTD (ms)
(b)

FIGURE 1. (a) The standard stereophonic setup according to Williams
[27], where g L and g R are the left and right channel gains and d L and d R
are the left and right channel delays, respectively, and (b) the associated
psychoacoustical curves representing the ICTD and ICLD that are necessary to pan the direction of a virtual source from the direction of the left
loudspeaker to the right one.

corresponding physical source (i.e., a loudspeaker), and 2) it provides a better externalization of the simulated sources due to the
presentation being made over loudspeakers [24].

Two-channel stereophony
Two-channel stereophony is an alternative spatial audio technology that requires the minimal number of channels to produce the
impression of spatial sound. In its usual implementation, twochannel stereophony uses two loudspeakers, each at the same
distance from the listener, positioned 30° to either side of the
front direction, providing a frontal auditory scene within a base
angle of 60°. The ideal listening position, referred to as the sweet
spot, thus forms an equilateral triangle with the loudspeakers.
Two-channel stereophony creates the illusion of a sound source
in a given direction within the base angle by means of the interchannel time differences (ICTDs) and interchannel level differences (ICLDs) of the two channels over which the source signal
is presented. Figure 1(a) shows the standard stereophonic setup
and illustrates how the gains and delays of each channel are
linked to the ICTD and ICLD. Although it is intuitively clear that
the direction of the virtual source is pulled toward the loudspeaker that produces the louder and earlier version of the signal,
knowing the precise relationship between the perceived source
direction and the presented (ICTD and ICLD) pairs requires
extensive psychoacoustic measurements.
The first comprehensive study of the relationships between
ICTD and ICLD, termed stereophonic panning laws, was conducted by Franssen [25]. Another study, by Williams [26], combined earlier studies on ICTD and ICLD. The panning curves
presented in that study are now known as Williams's curves.
Williams's psychoacoustic curves are illustrated in Figure 1(b),
which shows curves of ICTD/ICLD pairs that create a virtual
source in the direction of the left loudspeaker (the blue curve)
and the right loudspeaker (the orange curve). ICTD/ICLD pairs
that are below or above the two curves are also localized at
the left and right loudspeaker, respectively. Virtual sources in
directions between the loudspeakers are then created by means
of ICTD/ICLD pairs that evolve along a line that connects two
points on the psychoacoustic curves.
Note that there are many different ICTD/ICLD pairs that
can create a virtual source in the same direction. Intensity stereophony is achieved when the ICTD is zero and only ICLDs
are used for generating the stereophonic auditory perspective. In Figure 1(b), intensity panning curves are associated
to the vertical axis, e.g., the dashed vertical line connecting
points AL and BL. An ICLD of ±18 dB is sufficient to pan a
virtual source exactly in the direction of the right or the left
loudspeaker. Time-of-arrival stereophony is achieved when
the ICLDs are zero and only ICTDs are used for generating
the stereophonic auditory perspective. In Figure 1(b), time-ofarrival panning curves are associated to the horizontal axis,
e.g., the dotted horizontal line connecting points CL and DL.
An ICTD of ±1.2 ms is sufficient to create a virtual source in
the direction of the right or the left loudspeaker.
Time-intensity stereophony is achieved when a combination of ICTDs and ICLDs is used. The solid line in the figure

IEEE Signal Processing Magazine

May 2017

Table of Contents for the Digital Edition of Signal Processing - May 2017