Biomedical Engineering Reference
In-Depth Information
FIGURE 4-14
Process of using
Laplace transforms
to determine the
time-domain
responses of
complex systems.
TABLE 4-5
Rules for Handling Laplace Transforms (Bolton 1992)
Time Domain
S (Laplace) Domain
f
1
(
t
)
+
f
2
(
t
)
F
1
(
s
)
+
F
2
(
s
)
f
1
(
t
)
−
f
2
(
t
)
F
1
(
s
)
−
F
2
(
s
)
af
(
t
)
aF
(
s
)
e
−
Ts
F
(
s
)
f
(
t
−
T
)
d
dt
f
(
t
)
sF
(
s
)
−
f
(
o
)
d
2
dt
2
df
(
0
)
dt
s
2
F
(
s
)
−
sf
(
f
(
t
)
)
−
0
d
n
dt
n
d
n
−
1
f
(
0
)
dt
n
−
1
s
n
F
(
s
)
−
s
n
−
1
f
(
0
)
···−
f
(
t
)
t
1
s
F
f
(
t
)
(
s
)
0
To solve differential equations using the Laplace transform method, perform the fol-
lowing steps:
•
Transform each term in the differential equation into its Laplace transform.
•
Perform the algebraic manipulation for a specific input (e.g., step, impulse, sine
wave).
