Biomedical Engineering Reference
In-Depth Information
Fig. 8.1
An illustrative
example of fitting the
Oustaloupfilteroforder
N
pz
20 to the frequency
response of the respiratory
admittance in one patient
=
×
(s
+
0
.
02358
)(s
+
0
.
1669
)(s
+
1
.
182
)(s
+
8
.
366
)(s
+
59
.
22
)(s
+
419
.
3
)
2968
)
s
10
4
s
10
5
s
10
6
×
(s
+
+
2
.
101
·
+
1
.
488
·
+
1
.
053
·
×
s
10
6
s
10
7
+
7
.
456
·
+
3
.
704
·
(8.12)
For the inverse DFT method, the same frequency response as for the Oustaloup
filter was used. The results from Fig.
8.2
show that the same type of impulse re-
sponse is obtained with either methods. Similar impulse responses are obtained for
the other data sets. However, the Oustaloup filter is a high-order transfer function,
containing coefficients which differ significantly in their magnitude. As such, the
transfer function from (
8.10
)-(
8.12
) may not always pose numerical stability, since
it contains coefficients which vary broadly in magnitude
10
−
8
,
10
7
.Theinverse
DFT is numerically stable by definition and can serve to simulate the output of the
respiratory system for any input signal.
Figure
8.3
shows the log-log plots of the averaged values for impulse response in
admittances for adults and for children groups, respectively. To the impulse response
of each patient, a power-law model as given by (
8.9
) has been identified and its
[
]
Fig. 8.2
Impulse responses for the adult healthy averaged data set (
left
) and for the healthy chil-
dren averaged data set (
right
)