Digital Signal Processing Reference
In-Depth Information
As an example of time shifting, consider
x[m] = a
m
cos
(pm/4)u[m].
The time-shifted signal
x[n - 3]
is
x
[
m
] delayed by three sample periods and is
given by
p(n
-
3)
4
pn
4
-
3p
4
x[n - 3] = a
n- 3
cos
¢
≤
u[n - 3] = a
n- 3
cos
¢
≤
u[n - 3].
Shown in Figure 9.10 is another signal
x
[
n
], along with
y
1
[n] = x[n - 2]
and
y
2
[n] = x[n + 1].
The
n
1
-axis and the
n
2
-axis are obtained from
;
.
m = n - 2 Q n
1
= m + 2
m = n + 1 Q n
2
= m - 1
Both the
n
1
-axis and the
n
2
-axis are plotted in Figure 9.10(a), and the trans-
formed signals are given in Figure 9.10(b) and (c).
m
x
[
n
]
3
2
1
m
n
4
3
2
1
0
123
2
1
0
1
2
3
4
5
n
1
m
2
5
4
3
2
10
1
2
n
2
m
1
(a)
y
1
[
n
]
x
[
n
2]
3
2
1
2
1
0
1
2
3
4
5
n
(b)
y
2
[
n
]
x
[
n
1]
3
2
1
5
4
3
2
(c)
1
0
1
2
n
Figure 9.10
Time-shifted signals.
