B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

204 ANGLE MODULATION AND DEMODULATION
<p(t) in Eq. (5. 1), the instantaneous angular frequency and the generalized angle are related via
de
w; (t) = -
dt
0(t) = 1:00
Wi (a) da
(5.2a)
(5.2b)
Now we can see the possibility of transmitting the information of m(t) by varying the angle 0 of
a carrier. Such techniques of modulation, where the angle of the carrier is varied in some manner
with a modulating signal m(t), are known as angle modulation or exponential modulation.
Two simple possibilities are phase modulation (PM) and frequency modulation (FM). In
PM, the angle 0(t) is varied linearly with m(t):
0(t) =W e t + 80 + k p
m(t)
where k p
is a constant and W e is the carrier frequency. Assuming 80
generality,
0, without loss of
(5 .3a)
The resulting PM wave is
(5.3b)
The instantaneous angular frequency Wi (t) in this case is given by
d0
k .
Wi (t) = - = W e + pm(t)
dt
(5.3c)
Hence, in PM, the instantaneous angular frequency Wi varies linearly with the derivative of
the modulating signal. If the instantaneous frequency Wi is varied linearly with the modulating
signal, we have FM. Thus, in FM the instantaneous angular frequency w; is
where k t
is a constant. The angle 0(t) is now
(5.4a)
0(t) = 1:00
[w e + ktm(a)] da
= W e t + k t
1:00
m(a) da
Here we have assumed the constant term in 0(t) to be zero without loss of generality. The FM
wave is
(5.5)