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. 5.5
The white noise gain of Case 1, 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.
We deduce that the white noise is amplified if
12
1/6
[(1
− α
3,1
)(1
− α
3,2
) (1
− α
3,3
)]
1/3
.
ωτ
0
<
(5.11)
The directivity factor of the third-order DMA is
3
1
ω
6
2
1
− e
ωτ
0
(1
− α
3,n
)
n=1
′
G
DN,3
[
h
(
ω
)] =
,
(5.12)
h
′H
(
ω
)
Γ
DN
(
ω
)
h
′
(
ω
)
where
1
sinc (
ωτ
0
) sinc (2
ωτ
0
) sinc (3
ωτ
0
)
sinc (
ωτ
0
)
1
sinc (
ωτ
0
) sinc (2
ωτ
0
)
Γ
DN
(
ω
)=
.
(5.13)
sinc(2
ωτ
0
) sinc (
ωτ
0
)
sinc (
ωτ
0
)
1
sinc(3
ωτ
0
) sinc(2
ωτ
0
) sinc (
ωτ
0
)
1
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