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Chapter 3 Elementary Signals
v
v S out
0
t
Figure 3.2. Waveform for v out as defined in relation (3.3)
The waveform of Figure 3.2 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.
3.2 The Unit Step Function u t
0
*
A well-known discontinuous function is the unit step function u t that is defined as
0
0 t 0
u t = ® (3.4)
0
¯ 1 t ! 0
It is also represented by the waveform of Figure 3.3.
u t
1 0
0 t
Figure 3.3. Waveform for u t
0
1
0
In the waveform of Figure 3.3, the unit step function u t changes abruptly from to at t = . 0
0
But if it changes at t = t 0 instead, it is denoted as u t – t 0 . Its waveform and definition are as
0
shown in Figure 3.4 and relation (3.5).
1
u t – 0 t 0
t
0 t 0
Figure 3.4. Waveform for u t – t 0
0
* In some books, the unit step function is denoted as ut , that is, without the subscript 0. In this text, however, we
will reserve the ut designation for any input.
3-2 Circuit Analysis II with MATLAB Applications
Orchard Publications
