Digital Signal Processing Reference
In-Depth Information
(b)
Find the final value of by
(i)
the final value property (Property 8 of Table 7.3);
(ii)
finding
(c)
Verify the partial-fraction expansions in part (a), using MATLAB.
v(t)
v(t) = l
-1
[V(s)].
7.10.
Given the Laplace transform
2s
+
1
s
2
V(s) =
+ 4
,
v(t), v(0
+
),
(a)
Find the initial value of
by
(i)
the initial value property;
(ii)
finding
(b)
Find the final value of
v(t) = l
-1
[V(s)].
v(t)
by
(i)
the final value property;
v(t) = l
-1
[V(s)].
(ii)
finding
7.11.
(a)
Given
l[u(t)] = 1/s,
use the multiplication-by-
t
property (Property 9 of Table 7.3)
to find
(b)
Repeat part (a) for
l[t].
l[ cos
bt] = s/(s
2
+ b
2
).
l[t cos
bt],
given
l[t * t
n- 1
],
l[t
n- 1
] = (n - 1)!/s
n
.
(c)
Repeat part (a) for
given
7.12.
Use the derivative property (Property 2 of Table 7.3) to find
l[cos
bt]
from
l[sin bt] = b/(s
2
+ b
2
).
7.13.
Find the inverse Laplace transforms of the functions given. Verify all partial-fraction
expansions by using MATLAB.
5
s(s + 2)
(a)
F(s) =
s + 3
s(s + 1)(s + 2)
(b)
F(s) =
10(s
+
3)
s
2
(c)
F(s) =
+ 25
3
s(s
2
+ 2s + 5)
(d)
F(s) =
7.14.
Find the inverse Laplace transforms of the functions given. Verify all partial-fraction
expansions by using MATLAB.
1
s
2
(s + 1)
(a)
F(s) =
1
s(s + 1)
2
(b)
F(s) =
1
s
2
(s
2
+ 4)
(c)
F(s) =
39
(s + 1)
2
(s
2
(d)
F(s) =
+ 4s + 13)
