Digital Signal Processing Reference
In-Depth Information
The ROCs of the two transforms on the right side have no regions of the
z
-plane in common;
hence, no values of
z
exist for which
z
b
[1]
is convergent. Consequently, the
z
-transform of
f[n] = 1
for all
n
does not exist.
■
We now give four useful definitions with respect to functions and the bilateral
z
-transform.
1.
A function
f [n]
is
right sided
if
f[n] = 0
for
n 6 n
0
,
where
n
0
can be a
positive or a negative integer. For example,
u[n + 10]
is right sided, because
0,
n 6-10
.
b
u[n + 10] =
1,
n G-10
A second example is given in Figure 11.14(a).
2.
A function
f [n]
is
left sided
if
f[n] = 0
for
n 7 n
0
,
where
n
0
can be a
positive or a negative integer. For example,
u[-n + 10]
is left sided, because
f
[
n
]
•••
•••
n
0
n
(a)
f
[
n
]
•••
n
0
•••
n
(b)
f
[
n
]
•••
•••
n
(c)
Figure 11.14
Examples for signals: (a) right sided; (b) left sided; (c) finite duration.
