Digital Signal Processing Reference
In-Depth Information
(c)
This function can be expressed as
f(t) = e
5t
[u(2 - t) - u(-1 - t)].
Use tables to find its bilateral transform and its ROC.
7.24.
Find the inverse Laplace transform of the function
s + 9
s(s + 1)
F(s) =
for the following regions of convergence:
(a)
(b)
(c)
(d)
Give the final values of the functions of parts (a), (b), and (c).
Re(s) 6-1
Re(s) 7 0
-1 6 Re(s) 6 0
7.25.
Given a Laplace Transform
(s + 3)
(s + 1)(s - 1)
,
X(s) =
complete the following:
(a)
Find all possible inverse bilateral Laplace transforms.
(b)
Sketch the region of convergence in each case.
(c)
Label each time function as causal, noncausal, or two-sided.
(d)
Label each time function as BIBO stable or not BIBO stable.
(e)
Give the final values of the functions for each case.
7.26.
You are given a transfer function
1
(s + a)(s + b)
,
H(s) =
where
H(s)
is the Laplace transform of a time function
h(t).
(a)
If were causal, over what range of values of
a
and
b
would the system be BIBO
stable? State the Region of Convergence.
(b)
If were two-sided, over what range of values of
a
and
b
would the system be
BIBO stable? State the region of convergence.
(c)
If were noncausal, over what range of values of
a
and
b
would the system be
BIBO stable? State the region of convergence.
h(t)
h(t)
h(t)
7.27.
Find the inverse Laplace transform of
s + 1
H(s) =
+ 6s + 8
,
s
2
where -4 6 Re(s) 6-2.
