Signal Processing - May 2017 - 45

where ra is the radius of the microphone
array and c is the speed of sound. Microphone directivity patterns C l (i) are designed such that the level differences
with which the sound wave is recorded
are equal to the level difference that, in
combination with the time differences as
given in the above, creates a perception of
the sound source in the direction i. One
way to achieve this is by designing C l (i)
to satisfy the following relationship:

15.5 cm

PSR Microphone
Array

sin ^i - (z l - b)h
C l +1 (i)
, (6)
=
C l (i)
sin ^(z l +1 + b) - ih
where b is selected in such a way that
FIGURE 5. A block diagram of a PSR system indicating a one-to-one correspondence between the
for i, which coincides with the direc- microphone and loudspeaker channels and no intermediate processing. (Figure used courtesy of [29].)
tion of one of the microphones, the level
difference is equal to the level difference
intensity-based PSR provides better locatedness of phantom
needed to create the perception of the sound wave in the direcsources than techniques based on intensity alone (shown in the
tion of the corresponding loudspeaker. That level difference is
bar charts in Figure 8), which is attributed to the higher natulabeled EL (or FL with the reversed sign) in Figure 1(b) for the
ralness of the presented binaural cues [54].
case where the maximal ICTD is 0.6 ms. Thus, as the direction
of the sound source moves between the two microphones, the
captured time and level differences traverse a curve connecting
two end points, illustrated by the straight line between points
EL and FL in Figure 1(b), which correspond to virtual sources in the directions of two corresponding loudspeakers.
Microphones are additionally required to satisfy the constant
power condition and C l (i) 2 + C l +1 (i) 2 = 1, z l # i # z l +1
and sufficiently high attenuation outside the sector between the
ra
axes of the two adjacent microphones, so that every sound wave
θ
is effectively recorded and rendered only by the pair of the two
φl +1
closest channels.
The degree to which time differences are present is conφl
trolled by the radius of the microphone array, which is present implicitly in the b factor in (6). In the special case where
b = 0, the system implements intensity stereophony based
FIGURE 6. Two neighboring elements of the microphone array used in the
PSR recording system. (Figure used courtesy of [29].)
on the tangent panning law. An example of a directivity pattern designed according to PSR principles for a five-channel,
uniformly spaced system for an array of with ra = 15 cm is
0 dB
shown in Figure 7, along with its second-order approximation
Intensity
and the polar pattern that corresponds to b = 0, which is the
-5 dB
PSR (Ideal)
pattern designed for intensity stereophony according to the
-10 dB
36°
PSR (Second Order)
tangent law.
-15 dB
The five-channel PSR system design based on intensity and
-20 dB
time-intensity principles as specified earlier in this section was
-0°
-180°
subjectively evaluated and compared with second-order Ambisonics in terms of subjective localization accuracy [29]. Figure 8 shows the results of a localization test carried out using
different recording/reproduction systems. The time-intensity
-36°
-144°
PSR technology performed well, especially at off-center listening positions, while it performed worse for localization at
-72°
-108°
lateral source directions, which is due to the fact that psychoacoustic curves for frontal presentation were used for all the
FIGURE 7. The directivity patterns of the PSR and intensity methods. Also
pairs of loudspeakers. Another set of tests considered the locatshown is the directivity pattern of a second-order implementation of the ideal
PSR directivity used in subjective evaluations. (Figure used courtesy of [29].)
edness of generated phantom sources and showed that time-
IEEE Signal Processing Magazine

May 2017

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