Digital Signal Processing Reference
In-Depth Information
0.8
1.6
(
b
)
(
a
)
0.7
1.4
Predicted
Predicted
0.6
1.2
0.5
1
0.4
0.8
Simulated
Simulated
0.3
0.6
0.2
0.4
Input Noise Var 2.8 deg sqr
0.28
0.03
5.7
0.1
0.2
0
0
0 0.2 0.4 0.6
Normalized Post-mixing Filter Cut-off,
F
out
0 0.2 0.4 0.6
Normalized Post-mixing Filter Cut-off,
F
out
Figure 7.29
Noise performance of PM Scheme 2 Hilbert demodulator. (a) Input noise on
s
(measurement) channel only. (b) Input noise on both
s
(measurement) and
c
(reference) channel.
FM demodulation, is given by
4
2
3
diff
2
2
σ
≈
F
F
F
π
σ
(7.39)
ϕ
&
in
out
ε
3
where
F
diff
is the bandwidth of the first-order differentiator.
Table 7.2
Hilbert Demodulation Scheme 2
Noise Simulation Conditions and Results
Parameter
Symbol
Value
Filter Length (all)
L
+1
155
Cut-off Frequency on Premixing Filters
F
in
0.7
30
o
Modulation Amplitude
ϕ
o
Carrier Frequency
F
carrier
0.4
Cut-off Frequency on Postmixing Filters
F
out
0.25
Modulation Frequency
F
mod
0.025
x10
-6
Peak-to-Peak error
Single-Channel Noise Slope
Predicted Slope
(
a
)
2
F
in
F
out
0.35
Measured Slope
(
a
)
0.354
Double-Channel Noise Slope
Predicted Slope
(
a
)
4
F
in
F
out
0.7
Measured Slope
(
a
)
0.712
Predicted Single-Channel Noise Slope
(
b
)
2
F
in
1.4
Predicted Double-Channel Noise Slope
(
b
)
4
F
in
2.8
(
a
)
σ
ϕ
2
plotted against
2
using (7.34) and (7.38)
σ
ε
(
b
)
σ
ϕ
2
/
2
plotted against
F
out
using (7.34) and (7.38)
σ
ε
