3.5
3
2.5
2
1.5
1
0.5
0
–0.5
–1
–1.5
0 10 20
Time (Sampled)
Amplitude
Regularized
Impulse Response Estimates
Ordinary
30 40 50
(a) Regularized and ordinary estimates
3.5
3
2.5
2
1.5
1
0.5
0
–0.5
–1
–1.5
0 10 20
Time (Sampled)
Amplitude
Regularized
IR Estimates and True Values
True
30 40 50
(b) Regularized estimates and true coefficients
FIGURE 20.2
Estimates of IR coefficients with regularization for the proces s in Example 20.2.
−30 −20 −10 0 10 20 30
−0.2
0
0.2
0.4
0.6
lag
ρ
ε u
[l]
0 5 10 15 20 25
−0.5
0
0.5
1
lag
ρ
ε ε
[l]
(a) Residua l correlation plots
0 5 10 15 20
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
ACF of Input
Lags
(b) ACF of inputs
FIGURE 22.7
Residual analysis of the model and ACF of the inputs used in Example 22.5.
0 2 4 6 8 10 12
−1
0
1
2
3
4
5
6
Log of Singular Values
Model Order
Red: Default Choice (2)
Select Model Order in Command Window.
FIGURE 23.5
Plot of Hankel singular values for the system in Ex ample 23.6.
0 2 4 6 8 10 12
−1
0
1
2
3
4
5
Log of Singular Values
Model Order
Red: Default Choice (2)
Select Model Order in Command Window.
FIGURE 24.10
Plot of Hankel singular values.
FIGURE 24.11
Loss functions for ARX models with different numerator and denomina tor poly nomial
orders.
0 2 4 6 8 10 12
−1
0
1
2
3
4
5
6
Log of Singular Values
Model Order
Red: Default Choice (2)
FIGURE 24.19
Hankel singular values.
1
Amplitude
Period
Spectral Density
4
8
16
32
64
00.2 50 100 150 200 250
1/8
1/4
1/2
1
2
4
4
8
16
32
64
8
0.4
0.5
0
–0.5
50 100 150 200 250
(a) Sine wave corrupted by an impulse
10
Amplitude
Period
Spectral Density
8
4
16
32
64
128
8
4
16
32
64
128
0 100 200 300
Time
400 500
1/16
1/8
1/4
1/2
1
2
4
8
16
5
0
–10
100 200 300 400 500
(b) Industrial control loop measurement
FIGURE 25.4
Normalized sc alograms of two different signals.
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