Chapter 1
Elementary Signals
1
−
2
Signals and Systems with MATLAB
Computing and Simulink
Modeling, Fourth Edition
Copyright
©
Orchard Publications
We can express (1.3) by the waveform shown in Figure 1.2.
Figure 1.2.
Waveform for
as defined in relation (1.3)
The waveform of Figure 1.2 is an example of a discontinuous function. A function is said to be
dis-
continuous
if it exhibits points of discontinuity, that is, the function jumps from one value to
another without taking on any intermediate values.
1.2
The Unit Step Function
A well known discontinuous function is the
unit step function
*
which is defined as
(1.4)
It is also represented by the waveform of Figure 1.3.
Figure 1.3.
Waveform for
In the waveform of Figure 1.3, the unit step function
changes abruptly from
to
at
. But if it changes at
instead, it is denoted as
. In this case, its waveform and
definition are as shown in Figure 1.4 and relation (1.5) respectively.
Figure 1.4.
Waveform for
*
In some books, the unit step function is denoted as
, that is, without the subscript 0. In this text, however, we
will reserve the
designation for any input when we will discuss state variables in Chapter 5.
0
v
out
v
S
t
v
out
u
0
t
( )
u
0
t
( )
u t
( )
u t
( )
u
0
t
( )
0
t
0
<
1
t
0
>
=
u
0
t
( )
0
1
t
u
0
t
( )
u
0
t
( )
0
1
t
0
=
t
t
0
=
u
0
t
t
0
–
(
)
1
t
0
0
u
0
t
t
0
–
(
)
t
u
0
t
t
0
–
(
)

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