Microphone array
A microphone array, comprising N microphones, wherein N is greater than or equal to 3 is provided. The microphones are substantially equiangularly arranged over a circular arc subtending an angle ε, wherein ε is less than or equal to 2π, with the directional axes of the N microphones facing substantially radially outwards. Each of the N microphones have a substantially common directivity function Γ(θ) defining the directional response of the microphone, wherein θ=0 is the directional axis, and the directivity function Γ(θ) is arranged such that a sound source in acoustical free field is effectively captured by no more than two consecutive microphones in the array. By arranging the directivity function in this manner crosstalk between non-adjacent microphones can be minimized, which has been shown to improve auditory localization performance.
1. A microphone array, comprising:
N microphones, wherein N is greater than or equal to 3, arranged over a circular arc subtending an angle ε, wherein ε is less than or equal to 2π, with the directional axes of the N microphones facing substantially radially outwards,
the N microphones having respective non-cardioid directivity functions Γ m (θ) defining the directional response thereof, wherein θ=0 defines the directional axes;
wherein the directivity functions Γ m (θ) are arranged such that for adjacent microphones in the array the directivity functions Γ m (θ) thereof at least partially overlap, wherein a sound source in acoustical free field, situated at angle θ, wherein
ɛ
m
N
≤
θ
≤
ɛ
(
m
+
1
)
N
,
is effectively captured by no more than two adjacent microphones m and m+1 in the array at a level that when the effectively captured signal is reproduced it is significant to spatial auditory perception; and
wherein the directivity functions Γ m (θ) are further arranged such that the array response approximates a stereophonic panning curve for the sound source in direction of incidence θ between adjacent microphones m and m+1 in the array.
2. A microphone array according to claim 1 , wherein the directivity functions Γ m (θ) are further arranged such they are at least 15 dB below the value at the directional axis (θ=0), i.e.
20
log
10
(
Γ
(
0
)
Γ
(
θ
)
)
≥
15
for
θ
>
ɛ
N
and
θ
<
-
ɛ
N
.
3. A microphone array according to claim 1 , wherein the stereophonic panning curve approximates an intensity panning curve.
4. A microphone array according to claim 3 , wherein the directivity functions Γ m (θ) are substantially given by:
Γ
m
(
θ
)
=
T
(
ɛ
/
(
2
N
)
-
θ
)
1
+
T
(
ɛ
/
(
2
N
)
-
θ
)
where:
T
(
ϕ
)
=
[
tan
ϕ
+
tan
(
ϕ
0
/
2
)
tan
(
ϕ
0
/
2
)
-
tan
ϕ
]
2
or
T
(
ϕ
)
=
[
sin
ϕ
+
sin
(
ϕ
0
/
2
)
sin
(
ϕ
0
/
2
)
-
sin
ϕ
]
2
.
5. A microphone array according to claim 1 , wherein the array response approximates a stereophonic time-intensity panning curve.
6. A microphone array according to claim 5 , wherein the stereophonic time-intensity curves relate inter-channel time delays (τ) and channel intensity ratio to perceived auditory image position.
7. A microphone array according to claim 6 , wherein the stereophonic time-intensity curve comprises functions L(τ) and R(τ) which are the inter-channel level differences with respect to inter-channel time delay that are necessary to pan a stereophonic image towards a left loudspeaker or a right loudspeaker of a pair of loudspeakers, respectively.
8. A microphone array according to claim 7 , wherein the directivity functions Γ m (θ) are substantially given by Γ m (θ)=g(τ(θ)), where τ(θ) is the inter-channel time delay (ICTD) due to a plane wave incident on the microphone array at an angle θ, and where:
g
(
τ
)
=
K
2
(
τ
)
K
2
(
τ
)
+
1
with
K
(
τ
)
=
10
f
(
k
0
;
τ
)
10
and ƒ(k 0 ;τ) is a monotonic function of τ, parameterized by
k
0
=
R
(
τ
max
)
-
L
(
-
τ
max
)
2
τ
max
;
where
:
τ
max
=
-
2
r
m
c
sin
2
(
ɛ
2
N
)
;
and
τ
(
θ
)
=
2
r
m
c
sin
(
ɛ
2
N
)
sin
(
θ
-
ɛ
2
N
)
for
-
ɛ
N
≤
θ
≤
ɛ
N
,
where c is the speed of sound, r m is the radius of the microphone array, and ƒ(k 0 ;τ)=k 0 τ.
9. A panoramic audio recording system comprising:
a microphone array according to claim 1 , and
an N channel audio recorder arranged to record synchronously the respective audio signals captured at each of the N microphones in the microphone array.
10. A microphone array according to claim 1 , wherein the N microphones are substantially equiangularly arranged over the circular arc subtending an angle ε, the N microphones having a substantially common directivity function Γ m (θ) defining the directional response thereof.
11. A method arranged to:
provide N non-cardioid directivity functions Γ m (θ), wherein N is greater than or equal to 3, arranged over a circular arc subtending an angle ε, wherein ε is less than or equal to 2π, wherein θ=0 defines the directional axes,
wherein the N non-cardioid directivity functions Γ m (θ) define respective directional acoustic responses;
wherein the directivity functions Γ m (θ) are arranged such that adjacent directivity functions Γ m (θ) at least partially overlap, wherein a sound source in acoustical free field, situated at angle θ, wherein
ɛ
m
N
≤
θ
≤
ɛ
(
m
+
1
)
N
,
is effectively captured by no more than two adjacent directivity functions Γ m (θ) m and m+1 at a level that when the effectively captured signal is reproduced it is significant to spatial auditory perception; and
wherein the directional response of the directivity functions Γ m (θ) are further arranged to approximate a stereophonic panning curve in direction of incidence θ between adjacent directivity functions Γ m (θ) m and m+1.
12. A method according to claim 11 , wherein the directivity functions Γ m (θ) are further arranged such they are at least 15 dB below the value at the directional axis (θ=0), i.e.
20
log
10
(
Γ
(
0
)
Γ
(
θ
)
)
≥
15
for
θ
>
ɛ
N
and
θ
<
-
ɛ
N
.
13. A method according to claim 11 , wherein the stereophonic panning curve approximates an intensity panning curve.
14. A method according to claim 13 , wherein the directivity functions Γ m (θ) are substantially given by:
Γ
m
(
θ
)
=
T
(
ɛ
/
(
2
N
)
-
θ
)
1
+
T
(
ɛ
/
(
2
N
)
-
θ
)
where:
T
(
θ
)
=
[
tan
ϕ
+
tan
(
ϕ
0
/
2
)
tan
(
ϕ
0
/
2
)
-
tan
ϕ
]
2
or
T
(
ϕ
)
=
[
sin
ϕ
+
sin
(
ϕ
0
/
2
)
sin
(
ϕ
0
/
2
)
-
sin
ϕ
]
2
.
15. A method according to claim 11 , wherein the stereophonic panning curve approximates stereophonic time-intensity panning curves.
16. A method according to claim 15 , wherein the stereophonic time-intensity curve relates inter-channel time delays (τ) and channel intensity ratio to perceived auditory image position.
17. A method according to claim 16 , wherein the stereophonic time-intensity curve comprises functions L(τ) and R(τ) which are the inter-channel level differences with respect to inter-channel time delay that are necessary to pan a stereophonic image towards a left loudspeaker or a right loudspeaker of a pair of loudspeakers, respectively.
18. A method according to claim 17 , wherein the directivity functions Γ m (θ) are substantially given by Γ m (θ)=g(τ(θ)), where τ(θ) is the inter-channel time delay (ICTD) due to a plane wave incident at an angle θ, and where:
g
(
τ
)
=
K
2
(
τ
)
K
2
(
τ
)
+
1
with
K
(
τ
)
=
10
f
(
k
0
;
τ
)
10
and ƒ(k 0 ;τ) is a monotonic function of τ, parameterized by
k
0
=
R
(
τ
max
)
-
L
(
-
τ
max
)
2
τ
max
;
where
:
τ
max
=
-
2
r
m
c
sin
2
(
ɛ
2
N
)
;
and
τ
(
θ
)
=
2
r
m
c
sin
(
ɛ
2
N
)
sin
(
θ
-
ɛ
2
N
)
for
-
ɛ
N
≤
θ
≤
ɛ
N
,
where c is the speed of sound, r m is the radius between the origins of opposing directivity functions, and ƒ(k 0 ;τ)=k 0 τ.
19. A method arranged to:
capture N signals, wherein N is greater than or equal to 3, arranged over a circular arc subtending an angle ε, wherein ε is less than or equal to 2π, with the directional axes of the N signals facing substantially radially inwards,
wherein capturing the N signals includes providing non-cardioid directivity functions Γ m (θ) defining the directional responses to the N signals, wherein θ=0 is the directional axis;
wherein the directivity functions Γ m (θ) are arranged such that for adjacent signals in the array of signals the directivity functions Γ m (θ) thereof at least partially overlap, wherein a sound source in acoustical free field, situated at angle θ, wherein
ɛ
m
N
≤
θ
≤
ɛ
(
m
+
1
)
N
,
relates to no more than two captured signals m and m+1 in the array at a level that when the effectively captured signal is reproduced it is significant to spatial auditory perception; and
wherein the directivity functions Γ m (θ) are further arranged such that they approximate a stereophonic panning curve in the direction of incidence θ between adjacent signals m and m+1.