Digital Signal Processing Reference
In-Depth Information
t
ðÞ
g
i
¼½
y
i
k
1
;
y
i
k
2
;
u
i
k
;
u
i
k
1
;
u
i
k
2
and
p
t
¼½
a
1
;
a
2
;
b
1
;
b
2
;
b
3
. For brevity,
where
we drop the subscript k and write (4.42) as
!
1
!
:
X
X
N
i
¼
1
g
N
i
¼
1
g
i
t
i
i
y
i
p
N
¼
g
ð
4
:
43
Þ
Steady-state measurement using a sweep frequency input signal offers several
advantages over transient measurements such as the impulse response technique or
time domain techniques [3]. Here are some of the advantages:
1. Less precise instrumentation is required for steady-state measurements than for
transient measurements.
2. Collecting more data points improves the SNR for steady-state sweep frequency
measurements, but not for transient measurements.
3. Steady-state measurements offer these advantages at the expense of longer
measurement time.
4.9.0.1 Simulation Results
For the purpose of simulation, we consider a system with
252z
1
126z
2
B
ð
z
Þ¼
0
:
126
þ
0
:
þ
0
:
;
ð
4
:
44
Þ
A
ð
z
Þ¼
1
0
:
89944z
1
þ
0
:
404496z
2
ð
4
:
45
Þ
and we obtain output y
k
as
u
k
þ
k
:
B
ð
z
Þ
A
ð
z
Þ
y
k
¼
ð
4
:
46
Þ
A moving-window DFT was used to monitor y
k
until steady-state conditions were
obtained. Then (4.43) was used to obtain the solution. Results are tabulated
in Table 4.1. It is also possible to estimate the order of the system using this
algorithm [4].
Table 4.1 Measurements obtained using the set-up in Figure 4.17
i
1
2
3
4
5
6
7
8
9
10
if
i
=
N
0.01
0.05
0.09
0.13
0.17
0.21
0.25
0.29
0.33
0.37
A
i
0.995
1.002
1.09
1
0.647
0.435
0.237
0.19
0.087 0.098
'
i
Deg
4.73
25.5
47.3
82.7
113.5
131.9
141.2
149.0
24.2
34.9
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