Digital Signal Processing Reference
In-Depth Information
θ
2
1
δ
τ
0
−
+
1
Ω
FIG. 3.6
Implementation of the first-order cardioid.
The white noise gain is
(
ω
)] =
1
2
2
1
− e
2
ωτ
0
′
G
WN,1
[
h
=1
−
cos(2
ωτ
0
)
= 2 [1
−
cos(
ωτ
0
)][1+cos(
ωτ
0
)]
.
(3.27)
Figure 3.8 gives plots of
G
WN,1
[
h
(
ω
)] from (3.27), as a function of frequency,
for different values of
δ
. As explained in the previous section, the white noise
can be amplified, especially at low frequencies. Indeed, for small values of
ωτ
0
, we have
′
(
ω
)]
≈
2(
ωτ
0
)
2
′
G
WN,1
[
h
(3.28)
√
and the white noise is amplified if
ωτ
0
<
2
/
2. We can expect amplification
for a larger range of frequencies with the dipole than with the cardioid (the
different figures confirm this point).
We easily compute the directivity factor:
2
1
− e
2
ωτ
0
′
G
DN,1
[
h
(
ω
)] =
2 [1
−
sinc (
ωτ
0
) cos(
ωτ
0
)]
1
−
cos(2
ωτ
0
)
1
−
sinc (
ωτ
0
)cos(
ωτ
0
)
.
=
(3.29)
Search WWH ::
Custom Search