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. 4.13
The white noise gain of the second-order supercardioid, as a function of fre-
quency, for different values of
Δ
: (a)
Δ
= 1 cm, (b)
Δ
= 2 cm, (c)
Δ
= 3 cm, and (d)
Δ
= 5 cm.
(1
− α
2,1
)
2
(1
− α
2,2
)
2
α
2,1
+
α
2,2
+4
α
2,1
α
2,2
+
3
′
G
DN,2
[
h
(
ω
)]
≈
3
.
5
+
1
2
α
2,1
+
1
2
α
2,2
+3
α
2,1
α
2,2
(4.33)
′
Figure 4.15 shows a three dimensional plot of
G
DN,2
[
h
(
ω
)] from (4.33). We
deduce that the theoretical values of the directivity factor for the second-
order DMAs studied in this section are as follows.
′
•
Cardioid:
G
DN,2
[
h
(
ω
)]
≈
5
.
7.
′
•
Hypercardioid:
G
DN,2
[
h
(
ω
)]
≈
6
.
2.
′
•
Supercardioid:
G
DN,2
[
h
(
ω
)]
≈
5
.
9.
′
•
Quadrupole:
G
DN,2
[
h
(
ω
)]
≈
1
.
25.
′
(
ω
)] from (4.31), for
the cardioid, hypercardioid, supercardioid, and quadrupole, respectively, as
a function of frequency, for different values of
δ
.
For a point noise source, we find that the gain is
In Figs. 4.16, 4.17, 4.18, and 4.19, we plot
G
DN,2
[
h
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