Binaural rendering of a multi-channel audio signal
Binaural rendering a multi-channel audio signal into a binaural output signal is described. The multi-channel audio signal has a stereo downmix signal into which a plurality of audio signals are downmixed, and side information having a downmix information, as well as object level information of the plurality of audio signals and inter-object cross correlation information. Based on a first rendering prescription, a preliminary binaural signal is computed from the first and second channels of the stereo downmix signal. A decorrelated signal is generated as an perceptual equivalent to a mono downmix of the first and second channels of the stereo downmix signal being, however, decorrelated to the mono downmix. Depending on a second rendering prescription, a corrective binaural signal is computed from the decorrelated signal and the preliminary binaural signal is mixed with the corrective binaural signal to obtain the binaural output signal.
1. An apparatus for binaural rendering a multi-channel audio signal into a binaural output signal, the multi-channel audio signal comprising a stereo downmix signal into which a plurality of audio signals are downmixed, and side information comprising a downmix information indicating, for each audio signal, to what extent the respective audio signal has been mixed into a first channel and a second channel of the stereo downmix signal, respectively, as well as object level information of the plurality of audio signals and inter-object cross correlation information describing similarities between pairs of audio signals of the plurality of audio signals, the apparatus being configured to:
compute, based on a first rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, rendering information relating each audio signal to a virtual speaker position and HRTF parameters, a preliminary binaural signal from the first and second channels of the stereo downmix signal;
generate a decorrelated signal as a perceptual equivalent to a mono downmix of the first and second channels of the stereo downmix signal, the decorrelated signal being, however, decorrelated from the mono downmix;
compute, depending on a second rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, the rendering information and the HRTF parameters, a corrective binaural signal from the decorrelated signal; and
mix the preliminary binaural signal with the corrective binaural signal to acquire the binaural output signal.
2. The apparatus according to claim 1 , wherein the apparatus is further configured to, in generating the decorrelated signal,sum the first and second channel of the stereo downmix signal and decorrelate the sum to acquire the decorrelated signal.
3. The apparatus according to claim 1 further configured to:
estimate an actual binaural inter-channel coherence value of the preliminary binaural signal;
determine a target binaural inter-channel coherence value; and
set a mixing ratio determining to which extent the binaural output signal is influenced by the first and second channels of the stereo downmix signal as processed by the computation of the preliminary binaural signal and the first and second channels of the stereo downmix signal as processed by the generation of a decorrelated signal and the computation of the corrective binaural signal, respectively, based on the actual binaural inter-channel coherence value and the target binaural inter-channel coherence value.
4. The apparatus according to claim 3 wherein the apparatus is further configured to, in setting the mixing ratio, set the mixing ratio by setting the first rendering prescription and the second rendering prescription based on the actual binaural inter-channel coherence value and the target binaural inter-channel coherence value.
5. The apparatus according to claim 3 , wherein the apparatus is further configured to, in determining the target binaural inter-channel coherence value, perform the determination based on components of a target covariance matrix F=AEA*, with “*” denoting conjugate transpose, A being a target binaural rendering matrix relating the audio signals to the first and second channels of the binaural output signal, respectively, and being uniquely determined by the rendering information and the HRTF parameters, and E being a matrix being uniquely determined by the inter-object cross correlation information and the object level information.
6. The apparatus according to claim 5 , wherein the apparatus is further configured to, in computing the preliminary binaural signal, perform the computation so that
{circumflex over (X)} 1 =G·X
where X is a 2×1 vector the components of which correspond to the first and second channels of the stereo downmix signal, {circumflex over (X)} 1 is a 2×1 vector the components of which correspond to the first and second channels of the preliminary binaural signal, G is a first rendering matrix representing the first rendering prescription and comprising a size of 2×2 with
G
=
(
P
L
1
cos
(
β
+
α
)
exp
(
j
ϕ
1
2
)
P
L
2
cos
(
β
+
α
)
exp
(
j
ϕ
2
2
)
P
R
2
cos
(
β
-
α
)
exp
(
-
j
ϕ
1
2
)
P
R
2
cos
(
β
-
α
)
exp
(
-
j
ϕ
2
2
)
)
wherein, with xε{ 1 , 2 },
P
L
x
=
f
11
x
V
x
,
P
R
x
=
f
22
x
V
x
,
ϕ
x
=
{
arg
(
f
12
x
)
if
a
first
condition
applies
0
otherwise
wherein f 11 x , f 12 x and f 22 x are coefficients of sub-target covariance matrices F x of size 2×2 with F x =A E x A*,
wherein
e
ij
x
=
e
ij
(
d
i
x
d
i
1
+
d
i
2
)
(
d
j
x
d
i
1
+
d
i
2
)
are coefficients of N×N matrix E x , N being the number of audio signals, e ij are coefficients of the matrix E being of size N×N, and d i x are uniquely determined by the downmix information, wherein d i 1 indicates the extent to which audio signal i has been mixed into the first channel of the stereo downmix signal and d i 2 defines to what extent audio signal i has been mixed into the second channel of the stereo output signal,
wherein V x is a scalar with V x =D x E(D x )*+ε and D x is a 1×N matrix the coefficients of which are d i x ,
wherein the apparatus is further configured to, in computing a corrective binaural output signal, perform the computation such that
{circumflex over (X)} 2 =P 2 ·X d
where X d is the decorrelated signal, {circumflex over (X)} 2 is a 2×1 vector the components of which correspond to first and second channels of the corrective binaural signal, and P 2 is a second rendering matrix representing the second rendering prescription and comprising a size 2×2 with
P
2
=
(
P
L
sin
(
β
+
α
)
exp
(
j
arg
(
c
12
)
2
)
P
R
sin
(
β
-
α
)
exp
(
-
j
arg
(
c
12
)
2
)
)
wherein gains P L and P R are defined as
P
L
=
c
11
V
,
P
R
=
c
22
V
wherein c 11 and c 22 are coefficients of a 2×2 covariance matrix C of the preliminary binaural signal with
C={tilde over (G)}DED*{tilde over (G)}*
wherein V is a scalar with V=WEW*+ε, W is a mono downmix matrix of size 1×N the coefficients of which are uniquely determined by d i x ,
D
=
(
D
1
D
2
)
,
and {tilde over (G)} is
G
~
l
,
m
=
(
P
L
1
exp
(
j
ϕ
1
2
)
P
L
l
,
m
,
2
exp
(
j
ϕ
2
2
)
P
R
1
exp
(
-
j
ϕ
1
2
)
P
R
2
exp
(
-
j
ϕ
2
2
)
)
,
wherein the apparatus is further configured to, in estimating the actual binaural inter-channel coherence value, determine the actual binaural inter-channel coherence value as
ρ
C
=
min
(
c
12
c
11
c
22
,
1
)
wherein the apparatus is further configured to, in determining the target binaural inter-channel coherence value, determine the target binaural inter-channel coherence value as
ρ
T
=
min
(
f
12
f
11
fl
22
,
1
)
,
and
wherein the apparatus is further configured to, in setting the mixing ratio, determine rotator angles α and β according to
α
=
1
2
(
arccos
(
ρ
T
)
-
arccos
(
ρ
C
)
)
,
β
=
arctan
(
tan
(
α
)
P
R
-
P
L
P
L
+
P
R
)
,
with ε denoting a small constant for avoiding divisions by zero, respectively.
7. The apparatus according to claim 1 , wherein the apparatus is further configured to, in computing the preliminary binaural signal, perform the computation so that
{circumflex over (X)} 1 =G·X
where X is a 2×1 vector the components of which correspond to the first and second channels of the stereo downmix signal, {circumflex over (X)} 1 is a 2×1 vector the components of which correspond to the first and second channels of the preliminary binaural signal, G is a first rendering matrix representing the first rendering prescription and comprising a size of 2×2 with
G=AED *( DED *) −1 ,
where E is a matrix being uniquely determined by the inter-object cross correlation information and the object level information;
D is a 2×N matrix the coefficients d ij are uniquely determined by the downmix information, wherein d 1j indicates the extent to which audio signal j has been mixed into the first channel of the stereo downmix signal and d 2j defines to what extent audio signal j has been mixed into the second channel of the stereo output signal;
A is a target binaural rendering matrix relating the audio signals to the first and second channels of the binaural output signal, respectively, and is uniquely determined by the rendering information and the HRTF parameters,
wherein the apparatus is further configured to, in computing a corrective binaural output signal, perform the computation such that
{circumflex over (X)} 2 =P·X d
where X d is the decorrelated signal, {circumflex over (X)} 2 is a 2×1 vector the components of which correspond to first and second channels of the corrective binaural signal, and P is a second rendering matrix representing the second rendering prescription and comprising a size 2×2 and is determined such that PP*=ΔR, with ΔR=AEA*−G 0 DED*G 0 * with G 0 =G.
8. The apparatus according to claim 1 , wherein the apparatus is further configured to, in computing the preliminary binaural signal, perform the computation so that
{circumflex over (X)} 1 =G·X
where X is a 2×1 vector the components of which correspond to the first and second channels of the stereo downmix signal, {circumflex over (X)} 1 is a 2×1 vector the components of which correspond to the first and second channels of the preliminary binaural signal, G is a first rendering matrix representing the first rendering prescription and comprising a size of 2×2 with
G =( G 0 DED*G 0 *) −1 ( G 0 DED*G 0 *AEA*G 0 DED*G 0 *) 1/2 ( G 0 DED*G 0 *) −1 G 0 with G 0 =AED *( DED *) −1
where E is a matrix being uniquely determined by the inter-object cross correlation information and the object level information;
D is a 2×N matrix the coefficients d ij are uniquely determined by the downmix information, wherein d 1j indicates the extent to which audio signal j has been mixed into the first channel of the stereo downmix signal and d 2j defines to what extent audio signal j has been mixed into the second channel of the stereo output signal;
A is a target binaural rendering matrix relating the audio signals to the first and second channels of the binaural output signal, respectively, and is uniquely determined by the rendering information and the HRTF parameters,
wherein the apparatus is further configured to, in computing a corrective binaural output signal, perform the computation such that
{circumflex over (X)} 2 =P·X d
where X d is the decorrelated signal, {circumflex over (X)} 2 is a 2×1 vector the components of which correspond to first and second channels of the corrective binaural signal, and P is a second rendering matrix representing the second rendering prescription and comprising a size 2×2 and is determined such that PP*=(AEA*−GDED*G*)/V with V being a scalar.
9. The apparatus according to claim 1 , wherein the downmix information is time-dependent, and the object level information and the inter-object cross correlation information are time and frequency dependent.
10. A method for binaural rendering a multi-channel audio signal into a binaural output signal, the multi-channel audio signal comprising a stereo downmix signal into which a plurality of audio signals are downmixed, and side information comprising a downmix information indicating, for each audio signal, to what extent the respective audio signal has been mixed into a first channel and a second channel of the stereo downmix signal, respectively, as well as object level information of the plurality of audio signals and inter-object cross correlation information describing similarities between pairs of audio signals of the plurality of audio signals, the method comprising:
computing, based on a first rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, rendering information relating each audio signal to a virtual speaker position and HRTF parameters, a preliminary binaural signal from the first and second channels of the stereo downmix signal;
generating a decorrelated signal as a perceptual equivalent to a mono downmix of the first and second channels of the stereo downmix signal, the decorrelated signal being, however, decorrelated from the mono downmix;
computing, depending on a second rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, the rendering information and the HRTF parameters, a corrective binaural signal from the decorrelated signal; and
mixing the preliminary binaural signal with the corrective binaural signal to acquire the binaural output signal.
11. A non-transitory computer readable medium including a computer program comprising instructions for performing, when run on a computer, a method for binaural rendering a multi-channel audio signal into a binaural output signal, the multi-channel audio signal comprising a stereo downmix signal into which a plurality of audio signals are downmixed, and side information comprising a downmix information indicating, for each audio signal, to what extent the respective audio signal has been mixed into a first channel and a second channel of the stereo downmix signal, respectively, as well as object level information of the plurality of audio signals and inter-object cross correlation information describing similarities between pairs of audio signals of the plurality of audio signals, the method comprising: computing, based on a first rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, rendering information relating each audio signal to a virtual speaker position and HRTF parameters, a preliminary binaural signal from the first and second channels of the stereo downmix signal; generating a decorrelated signal as a perceptual equivalent to a mono downmix of the first and second channels of the stereo downmix signal, the decorrelated signal being, however, decorrelated from the mono downmix; computing, depending on a second rendering prescription depending on the inter-object cross correlation information, the object level information, the downmix information, the rendering information and the HRTF parameters, a corrective binaural signal from the decorrelated signal; and mixing the preliminary binaural signal with the corrective binaural signal to acquire the binaural output signal.