Digital Signal Processing Reference
In-Depth Information
10
10
0
0
−
10
−
10
−
20
−
20
−
30
−
30
−
40
−
40
−
50
−
50
−
60
−
60
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
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. 3.8
The white noise gain of the first-order cardioid, 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.
′
Figure 3.9 gives plots of
G
DN,1
[
h
(
ω
)] from (3.29), as a function of frequency,
for different values of
δ
. It can be verified that
′
′
G
DN,1
[
h
(
ω
)]
> G
WN,1
[
h
(
ω
)]
.
(3.30)
For small values of
ωτ
0
, we have
3
2(
ωτ
0
)
2
(
ω
)]
≈
2(
ωτ
0
)
2
·
′
G
DN,1
[
h
≈
3
,
(3.31)
which corresponds exactly to the theoretical value of the directivity factor
for a cardioid with diffuse noise [1].
Finally, to end this section, we give the gain for a point noise source:
Search WWH ::
Custom Search