Linear Signal and Systems [25] Find the inverse Laplace transform of
2
( ) 1 2 4 3 1 9
s
X s
s s s
= + + − − +
4
( )
( 1)( 3)
X s
s s
= + +
2
3
( ) 2 4 1
( 1)( 2)
s s
X s
s s
+ +
=
+ +
2
1
( )
( 3)( 2 5)
s
X s
s s s
+
= + + +
2 3
2
( )
( 5 4)
s s
X s se e
s s s
− −
+
=
+ +
Check your results using MATLAB … useful functions are ilaplace() and
partfrac() Linear Signal and Systems
- [10] If the output of a system is = cos 4 when an input,
= 10 , what is the transfer function of the system at hand?
- [10] Suppose the transfer function of a system is given by
H s( ) 2s6
s
= +
Calculate its impulse response and the output yZS(t) if the input is =
.
- [15] Use Laplace transform to solve the following differential equations (i.e.,
solve for y(t))
2
2 3 4 ( )
t
d y dy
y e u t
dt dt
−
+ − =
with y(0) = 1 and
(0) 0
dy
dt
=
2
2
6 25 2
d y dy dx
y x
dt dt dt
+ + = +
where x(t) = 25u(t) and ICs are y(0) = 1 and
dy(0) 1
dt
[25] Find the inverse Laplace transform of Linear Signal and Systems
2
( ) 1 2 4 3 1 9
s
X s
s s s
= + + − − +
4
( )
( 1)( 3)
X s
s s
= + +
2
3
( ) 2 4 1
( 1)( 2)
s s
X s
s s
+ +
=
+ +
2
1
( )
( 3)( 2 5)
s
X s
s s s
+
= + + +
2 3
2
( )
( 5 4)
s s
X s se e
s s s
− −
+
=
+ +
Check your results using MATLAB … useful functions are ilaplace() and
partfrac()
- [10] If the output of a system is = cos 4 when an input,
= 10 , what is the transfer function of the system at hand?
- [10] Suppose the transfer function of a system is given by
H s( ) 2s6
s
= +
Calculate its impulse response and the output yZS(t) if the input is =
.
- [15] Use Laplace transform to solve the following differential equations (i.e.,
solve for y(t))
2
2 3 4 ( )
t
d y dy
y e u t
dt dt
−
+ − =
with y(0) = 1 and
(0) 0
dy
dt
=
2
2
6 25 2
d y dy dx
y x
dt dt dt
+ + = +
where x(t) = 25u(t) and ICs are y(0) = 1 and
dy(0) 1
dt