Digital Signal Processing Reference
In-Depth Information
Θ
.
3
2
1
.
.
Δ
Δ
-
Τ
0
/
2
-
Τ
0
-
Τ
0
/
2
-
Τ
0
9
1
7
9
1
7
−
7
−
7
×
×
×
×
−
−
+
+
−
−
+
+
Τ
0
−
+
1
Ω
2
FIG. 4.25
Implementation of the second-order cardioid with one distinct null.
(4.40) as
2
(
ω
)
,θ
]
≈
C
2
1
2
+
1
′
B
[
h
2
cos
θ
,
(4.41)
where we recognize the pattern of the second-order cardioid with one distinct
null.
The white noise gain is
2
2
16
7
−
16
1
− e
2
ωτ
0
7
e
ωτ
0
/
2
′
G
WN,2
[
h
(
ω
)] =
,
(4.42)
D
WN,2
(
ω
)
where
D
WN,2
(
ω
)=2+
674
49
−
576
49
cos(
ωτ
0
/
2)
−
18
7
cos(2
ωτ
0
)+
32
7
cos(3
ωτ
0
/
2)
.
(4.43)
′
Figure 4.27 shows plots of
G
(
ω
)] from (4.42), as a function of fre-
quency, for different values of
δ
. For small values of
ωτ
0
, we get
WN,2
[
h
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