Digital Signal Processing Reference
In-Depth Information
7.28.
You are given a Laplace transform
1
(s + 10)(s + 5)(s - 3)
,
H(s) =
where
- 5 6 Re(s) 6 3.
Label each of the three poles as coming from a left-sided time function or right-sided
time function.
7.29.
In Chapter 3, direct convolution was used to solve for the output of LTI systems. For
the following inputs and impulse responses, find the output, using Laplace transforms:
x(t) = e
5t
u(t) and h(t) = u(t).
(a)
Problem 3.1(a)(ii), where
(b)
Problem 3.7(b), where
x(t) = e
-t
u(t) and h(t) = u(t - 2) - u(t - 4).
You may
find the time-shift property to be useful.
h(t) = e
t
u(t).
7.30.
You are given a system with impulse response
(a)
Is the system bounded-input bounded-output stable?
(b)
You now hook the system up into a
feedback
system, as shown in Figure P7.30.
Find the new system transfer function from the input to the output
(c)
Finally, find the range of the parameter
A
such that the system is bounded-input
bounded-output stable.
x(t)
y(t).
x
(
t
)
w
(
t
)
y
(
t
)
h
(
t
)
A
A
y
(
t
)
Figure P7.30
