Digital Signal Processing Reference
In-Depth Information
F
()
F
(
0
)
F
(
0
)
2
1
2
2
0
1
0
B
B
(a)
F
()
F
(0)
F
(
0
)
2
0
2
2
(b)
Figure 6.21
3-dB or half-power bandwidth.
where dB is the abbreviation for decibel. The term
half-p
o
wer
refers to the fact that
if the magnitude of voltage or current is divided by
2
2,
the power delivered to
a load by that signal is halved, because
2
R
= I
rms
V
rms
2
P =
R.
This is a widely used definition of bandwidth and one that most electrical engineer-
ing students are familiar with from their circuit analysis courses.
Null-to-null bandwidth,
or
zero-crossing bandwidth,
is shown in Figure 6.22. It
is defined as the range of frequencies The frequency of the first null
(zero magnitude) in the frequency spectrum above is labeled and for band-
pass signals, is the frequency of the first null below where is the frequen-
cy at which the spectrum has its maximum magnitude. For baseband signals such as
the one shown in Figure 6.22(b), For baseband signals, this definition of
bandwidth is sometimes called the
first-null bandwidth
.
Null-to-null bandwidth is applicable only to cases where there is a definite zero
value (null) in the magnitude frequency spectrum. However, it is a useful definition,
because some widely used waveforms—the rectangular pulse, for example—have
nulls in their frequency spectra.
B = v
2
- v
1
.
v
m
v
2
,
v
1
,
v
m
,
v
m
v
1
= 0.
