
84-16 Signal Processing
e carrier-quadrature form of Equation 84.22 is
f t A t t t t
s c m c m c
( ) cos[ sin( )]cos( ) sin[ sin( )]sin( )= −
β ω ω β ω ω
(8
4
.23
)
Unlike
AM
,
an FM sig
nal
co
ntains
bo
th
in
-phase
an
d
qu
adrature
co
mponents,
an
d
th
e
am
plitudes
of
both are nonlinear functions of the modulation index. e terms cos[β sin(ω
m
t)] and sin[β sin(ω
m
t)] are
ge
nerally
ex
panded
in te
rms
of Be
ssel
fu
nctions
(s
ee
Sc
hwartz
[3
]
fo
r
de
tailed
an
alysis)
. e Be
ssel
fu
nc-
tion
e
xpression
o
f
a
n
F
M
si
gnal
i
s
f t A J n t
n
n
s c c m
( ) ( )cos[( ) ]= +
=−∞
∞
∑
β ω ω
(8
4
.24
)
where J
n
(β) represents a Bessel function of the rst kind of order n. Beyer [23] provides