Digital Signal Processing Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1
−0.5
0
0.5
1
Real
Figure 2.15:
The complex power series 0.9
n
exp(j2
π
3
/N
)
n
where
N
=32and
n
= 0:1:
N
-1, plotted as
circles, and the same series, computed as 0.9
n
(cos
(
2
πn
3
/N)
+
j
sin
(
2
πn
3
/N)
), plotted as x's, which lie
inside the circles since the two methods of computation are equivalent.
2.4.15 ENERGY OF A SIGNAL
The energy of a sequence
x
[
n
]
is defined as
∞
∞
x
[
n
]
x
∗
[
n
]=
2
E
=
|
x
[
n
]|
n
=−∞
n
=−∞
where
x
∗
[
n
]
is the complex conjugate of
x
[
n
]
.If
E
is finite,
x
[
n
]
is called an
Energy Sequence
.
2.4.16 POWER OF A SIGNAL
The power of a signal over a number of samples is defined as
N
1
2
P
=
N
|
x
[
n
]|
(
2
N
+
1
)
n
=−
