Digital Signal Processing Reference
In-Depth Information
y
1
(
t
)
y
2
(
t
)
x
1
(
t
)
x
2
(
t
)
input
signals
output
signals
CT
System
input
signal
CT
system
output
signal
x
(
t
)
y
(
t
)
x
m
(
t
)
y
n
(
t
)
(a)
(b)
Fig. 2.1. General schematics of CT systems. (a) Multiple-input, multiple-output (MIMO) CT system with
m
inputs and
n
outputs. (b) Single-input, single-output CT system.
x
1
[
k
]
x
2
[
k
]
y
1
[
k
]
y
2
[
k
]
output
signals
input
signals
DT
system
DT
system
x
[
k
]
y
[
k
]
x
m
[
k
]
y
n
[
k
]
(a)
(b)
Fig. 2.2. General schematics of
DT systems. (a) Multiple-input,
multiple-output (MIMO) DT
system with
m
inputs and
n
outputs. (b) Single-input,
single-output DT system.
notation:
x
(
t
)
→
y
(
t
);
CT system
(2.1)
DT system
x
[
k
]
→
y
[
k
]
.
(2.2)
The arrow in Eq. (2.1) implies that a CT signal
x
(
t
), applied at the input of a
CT system, produces a CT output
y
(
t
). Likewise, the arrow in Eq. (2.2) implies
that a DT input signal
x
[
k
] produces a DT output signal
y
[
k
]. This chapter
focuses on the classification of CT and DT systems. Before proceeding with
the classification of systems, we consider several applications of signals and
systems in electrical networks, electronic devices, communication systems, and
mechanical systems.
The organization of Chapter 2 is as follows. In Section 2.1, we provide
several examples of CT and DT systems. We show that most CT systems can be
modeled by linear, constant-coefficient differential equations, while DT systems
can be modeled by linear, constant-coefficient difference equations. Section 2.2
introduces several classifications for CT and DT systems based on the properties
of these systems. A particularly important class of systems, referred to as linear
time-invariant (LTI) systems, consists of those that satisfy both the linearity and
time-invariance properties. Most practical structures are complex and consist
of several LTI systems. Section 2.3 presents the series, parallel, and feedback
configurations used to synthesize larger systems. Section 2.4 concludes the
chapter with a summary of the important concepts.
2.1 Examples of systems
In this section, we present examples of physical systems and derive relationships
between the input and output signals associated with these systems. For linear
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