Time Domain Representation of Continuous and Discrete Signals 11
R.1.20 A right-shifted unit step, by t 0 units, denoted by u(t − t 0 ) is illustrated in Figure 1.11.
The shifted step function u(t − t 0 ) is defi ned analytically by
ut t
tt
tt
()
(^0)
0
0
1
0
for
for
R.1.21 A unit step sequence or the discrete unit step u(n) is illustrated in Figure 1.12.
The unit discrete step u(n) is defi ned analytically by
un
n
n
()
10
00
for
for
R.1.22 A unit discrete step sequence u(n) can be constructed by a sequence of impulses
indicated as follows:
un n k
k
() ( )
0
∑
Observe that δ(n) = u(n) − u(n − 1).
R.1.23 A shifted and amplitude-scaled step sequence, A u(n − m) is illustrated in Figure 1.13.
The sequence A u(n − m) is defi ned analytically by
Au n m
Anm
nm
()
for
0 for
sw closes at t = 0
1 V v(t) = u(t)
FIGURE 1.10
Circuit implementation of u(t).
FIGURE 1.11
Plot of u(t − t 0 ).
u(t − t 0 )
(^0) t 0
t
1
u(n)
− 2 − (^11023)
n
FIGURE 1.12
Plot of u(n).