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
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)
(
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. 4.12
The white noise gain of the second-order hypercardioid, 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.
6
1/4
ωτ
0
<
(1
− α
2,1
)(1
− α
2,2
)
.
(4.30)
The directivity factor of the second-order DMA is
2
2
1
− e
ωτ
0
(1
− α
2,1
)
1
− e
ωτ
0
(1
− α
2,2
)
′
G
DN,2
[
h
(
ω
)] =
,
(4.31)
D
(
ω
)
where
D
(
ω
)=4
−
4 sinc(
ωτ
0
)cos(
ωτ
0
α
2,1
)
−
4 sinc(
ωτ
0
)cos(
ωτ
0
α
2,2
)
+ 2 cos[
ωτ
0
(
α
2,1
− α
2,2
)]
+2sinc(
ωτ
0
)cos(
ωτ
0
)cos[
ωτ
0
(
α
2,1
+
α
2,2
)]
.
(4.32)
Using Taylor's series, it can be shown that
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