Digital Signal Processing Reference
In-Depth Information
5
0
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
)
5
0
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. 3.9
The directivity factor 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.
2
1
− e
2
ωτ
0
′
G
NS,1
[
h
(
ω
)] =
2
1
− e
ωτ
0
(1+cos
θ
N
)
1
−
cos(2
ωτ
0
)
1
−
cos[
ωτ
0
(1+cos
θ
N
)]
,
=
(3.32)
′
∀f
for
θ
N
= 180
◦
. Figure 3.10 gives plots of
where
G
NS,1
[
h
(
ω
)] =
∞,
′
G
(
ω
)], as a function of
θ
N
, for several frequencies and two values of
δ
. For small values of
ωτ
0
, (3.32) becomes
NS,1
[
h
1
′
G
NS,1
[
h
(
ω
)]
≈
2
,
(3.33)
1
2
+
1
2
cos
θ
N
which corresponds to the theoretical gain of the first-order cardioid.
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