Graphics Programs Reference
In-Depth Information
where
is the amplitude modulation or envelope,
is the phase modu-
r
()
φ
x
()
lation,
is the carrier frequency, and both
and
have frequency com-
f
0
r
()
φ
x
()
ponents significantly smaller than
. The frequency modulation is
f
0
1
2π
d
φ
x
------
f
m
()
=
()
(3.2)
d
t
and the instantaneous frequency is
1
2π
d
------
f
i
()
=
(
2π
f
0
t
+
φ
x
()
)
=
f
0
+
f
m
()
(3.3)
d
t
If the signal bandwidth is
, and if
is very large compared to
, the signal
B
f
0
B
is referred to as a narrow band pass signal.
x
()
Band pass signals can also be represented by two low pass signals known as
the quadrature components; in this case Eq. (3.1) can be rewritten as
x
()
x
I
=
() 2π
f
0
t
cos
x
Q
() 2π
f
0
t
sin
(3.4)
where and are real LP signals referred to as the quadrature compo-
nents and are given, respectively, by
x
I
()
x
Q
()
x
I
()
r
() φ
x
=
cos
()
(3.5)
x
Q
()
r
() φ
x
=
sin
()
Fig. 3.1 shows how the quadrature components are extracted.
2 π
f
0
t
cos
x
I
()
LP Filter
mixer
x
()
x
I
=
() 2π
f
0
t
cos
x
Q
() 2π
f
0
t
sin
x
Q
()
mixer
LP Filter
2 π
f
0
t
sin
Figure 3.1. Extraction of quadrature components.
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