Digital Signal Processing Reference
In-Depth Information
x
2
(
t
)
3
2
1
t
5
4
3
2
1
0
1
2
3
4
5
6
Figure P2.28
2.28.
(a)
You are given an LTI system. The response of the system to an input
x
1
(t) = u(t) - u(t - 1)
is a function
y
1
(t).
What is the response of the system to the input
x
2
(t)
in
Figure P2.28 in terms of
(b)
You are given another LTI system with the input shown in Figure P2.28. Find the
output
y
1
(t)?
y
2
(t)
in terms of the system's output,
y
1
(t),
if
y
1
(t)
is in response to the input
x
1
(t) = 2u(t - 1) - u(t - 2) - u(t - 3).
2.29.
Determine whether
the ideal time delay
y(t) = x(t - t
0
)
is
(i)
memoryless,
(ii)
invertible,
(iii)
causal,
(iv)
stable,
(v)
time invariant, and
(vi)
linear.
2.30.
Let
h
(
t
) denote the response of a system for which the input signal is the unit impulse func-
tion
d(t).
Suppose that
h
(
t
) for a
causal
system has the given even part
h
e
(t)
for
t 7 0:
h
e
(t) = t[u(t) - u(t - 1)] + u(t - 1), t 7 0.
Find
h
(
t
) for all time, with your answer expressed as a mathematical function.
2.31.
(
a)
Sketch the characteristic
y
versus
x
for the system
y(t) = ƒ x(t) ƒ .
Determine
whether this system is
(i)
memoryless,
(ii)
invertible,
(iii)
causal,
(iv)
stable,
(v)
time invariant, and
(vi)
linear.
(b)
Repeat Part (a) for
x(t),
x Ú 0
b
y(t) =
x 6 0
.
0,
