PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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).