Time Domain Representation of Continuous and Discrete Signals
13
R.1.28 The more general analog ramp function r(t) = t u(t) (with time and amplitude scaled)
is defi ned by
Ar t t
At
t t
t t
(
)
Ϫ
Ն
Ͻ
0
0
0
0
ϭ
for
for



where A represents the ramp’s slope and t 0 is the time shift with respect to the
origin.
R.1.29 The discrete ramp sequence denoted by r(n − m) u(n − m) is defi ned analytically
by
r n m u n m
n
n m
n m
(
) (
)
Ϫ
Ϫ
Ն
Ͻ
ϭ
for
for
0



−6 −5 −4 −3 −2 −1
0
1
2
3
4
5
6
0
0. 5
1
1. 5
2
n
Amplitude
pul(n/11)
FIGURE 1.15
Plot of the function pul(n/11).
r(t )
t
1
1
0
FIGURE 1.16
Plot of the analog unit ramp function r(t) = t u(t).
CRC_47760_CH001.indd 13
CRC_47760_CH001.indd 13
7/25/2008 4:16:12 PM
7/25/2008 4:16:12 PM