Digital Signal Processing Reference
In-Depth Information
10
5
0
10
5
0
−
5
−
10
−
15
−
20
−
25
−
30
−
5
−
10
−
15
−
20
−
25
−
30
0
.
5
1
.
0
1
.
5 2
.
0 2
.
5 3
.
0 3
.
5
4
.
0
0
0
0
.
5 1
.
0 1
.
5 2
.
0 2
.
5
3
.
0 3
.
5 4
.
0
F
(kHz)
F
(kHz)
(
a)
(
b
)
10
5
0
10
5
0
−
5
−
10
−
15
−
20
−
25
−
30
−
5
−
10
−
15
−
20
−
25
−
30
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. 4.28
The directivity factor of the second-order cardioid with one distinct null, 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.
D
DN,2
(
ω
)=
772
49
−
576
49
cos(
ωτ
0
/
2)
−
18
7
cos(2
ωτ
0
)+
32
7
cos(3
ωτ
0
/
2)
−
18
7
+
32
+ sinc (
ωτ
0
)cos(
ωτ
0
)
7
cos(
ωτ
0
/
2)
520
49
cos(
ωτ
0
)+
160
49
cos(
ωτ
0
/
2)
−
288
−
sinc (
ωτ
0
)
49
cos(3
ωτ
0
/
2)
.
(4.47)
In Fig. 4.28, we plot
G
DN,2
[
h
′
(
ω
)] from (4.46), as a function of frequency, for
different values of
δ
.
Finally, to end this section, we give the gain for a point noise source:
2
2
16
7
−
16
1
− e
2
ωτ
0
7
e
ωτ
0
/
2
′
G
NS,2
[
h
(
ω
)] =
,
(4.48)
D
NS,2
(
ω
)
where
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