Biomedical Engineering Reference
In-Depth Information
1.5
1
e
-
t
0.5
y
(
t
) =
e
-
t
-
e
-4
t
0
0
1
2
3
4
5
6
e
-4
t
t (s)
-0.5
-1
-1.5
FIGURE 13.68
¼
e
t
-
e
4
t
, with functions
e
t
and
e
4
t
also shown.
Impulse response
y
(
t
)
EXAMPLE PROBLEM 13.12
Find z and o
n
for the impulse response shown in Figure 13.69.
0.6
0.5
0.4
0.3
0.2
01
0
0
5
10
15
20
25
30
t (s)
FIGURE 13.69
Illustration for Example Problem 13.12.
Solution
The data (solid line) is redrawn in Figure 13.70 with the exponential of the dominant time
constant extrapolated back to zero (dotted line). This gives an initial value of 1 for the exponential.
The response falls to 1 percent of 1 at approximately 25 s, giving 5
t
2
25, or
t
2
¼
5 s for the
dominant time constant and
s
2
¼
0.2.
