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. 3.3
The white noise gain of the first-order dipole, 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
′H
(
ω
)
d
(
ω,
1)
h
′
G
DN,1
[
h
(
ω
)] =
h
′H
(
ω
)
Γ
DN
(
ω
)
h
′
(
ω
)
|
1
− e
ωτ
0
|
2
2 [1
−
sinc (
ωτ
0
)]
=
1
−
cos(
ωτ
0
)
=
1
−
sinc (
ωτ
0
)
.
(3.14)
Figure 3.4 gives plots of
G
DN,1
[
h
′
(
ω
)] from (3.14), as a function of frequency,
for different values of
δ
.
We easily see that
′
′
G
DN,1
[
h
(
ω
)]
> G
WN,1
[
h
(
ω
)]
.
(3.15)
Also, for small values of
ωτ
0
, (3.14) becomes
(
ω
)]
≈
(
ωτ
0
)
2
2
3!
(
ωτ
0
)
2
′
G
DN,1
[
h
·
≈
3
,
(3.16)
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