12 Practical MATLAB® Applications for Engineers
R.1.24 The analog pulse function pul(t/τ) is illustrated graphically in Figure 1.14.
The function pul(t/τ) is defi ned analytically by
pul t
t
tt
(/ )
//
//
1for
for and
22
02 2
R.1.25 The analog pulse pul(t/τ) is related to the analog step function u(t) by the following
relation:
pul(t/) = u(t + /2) − u(t − /2)
R.1.26 The discrete pulse sequence denoted by pul(n/N) is given by
pul n N
Nn
Nn n
(/ )
//
//
1for
for and
22
02 2
N
N
For example, for N = 11 (odd), the discrete sequence is given by
pul n
n
nn
(/ ) 11
15 5
05 5
for
for
and
The preceding function pul(n/11) is illustrated in Figure 1.15.
Observe that the pulse function pul(n/11) can be represented by the superposition
of two discrete step sequences as
pul(n/11) = u(n + 5) − u(n − 6)
R.1.27 The analog unit ramp function denoted by r(t) = t u(t) is illustrated in Figure 1.16.
The unit ramp is defi ned analytically by
rt
tt
t
()
for
for
0
00
A
u(n − m)
m − 1 mm + 1m + 2m + 3
n
FIGURE 1.13
Plot of u(n − m).
pul(t/)
t
−/2 0 /2
1
FIGURE 1.14
Plot of pul(t/τ).