Digital Signal Processing Reference
In-Depth Information
10
10
0
0
−
10
−
10
−
20
−
20
−
30
−
30
−
40
−
40
−
50
−
50
−
60
−
60
−
70
−
70
−
80
−
80
0
.
5
1
.
0
1
.
5
2
.
0
2
.
5 3
.
0 3
.
5
4
.
0
0
0
.
5
1
.
0 1
.
5 2
.
0 2
.
5 3
.
0
3
.
5 4
.
0
0
F
(kHz)
F
(kHz)
(
a
)
(
b
)
10
10
0
0
−
10
−
10
−
20
−
20
−
30
−
30
−
40
−
40
−
50
−
50
−
60
−
60
−
70
−
70
−
80
−
80
0
0
.
5 1
.
0 1
.
5 2
.
0 2
.
5 3
.
0 3
.
5 4
.
0
0
0
.
5 1
.
0 1
.
5 2
.
0 2
.
5 3
.
0 3
.
5 4
.
0
F
(kHz)
F
(kHz)
(c)
(d)
FIG. 4.3
The white noise gain of the second-order dipole, as a function of frequency, for
different values of
Δ
: (a)
Δ
= 1 cm, (b)
Δ
= 2 cm, (c)
Δ
= 3 cm, and (d)
Δ
= 5 cm.
(
ω
)]
≈
2
(
ωτ
0
)
4
4
10
(
ωτ
0
)
4
′
G
DN,2
[
h
·
≈
5
,
(4.16)
which should correspond to the theoretical value of the directivity factor
for the second-order dipole with diffuse noise
1
. We observe that this gain is
almost two times larger than the first-order dipole gain.
For a point noise source, the gain of the second-order dipole is
2
′H
(
ω
)
d
(
ω,
1)
h
′
G
NS,2
[
h
(
ω
)] =
|h
′H
(
ω
)
d
(
ω,
cos
θ
N
)
|
2
|
1
− e
ωτ
0
|
4
=
4
1
− e
ωτ
0
cos
θ
N
[1
−
cos(
ωτ
0
)]
2
[1
−
cos(
ωτ
0
cos
θ
N
)]
2
.
=
(4.17)
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