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 )
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