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

208 ANGLE MODULATION AND DEMODULATION
Figure 5.5
FM and PM
waveforms.
1
--t----
-t m:: J -I1- (a)
m(t)
--!---
1 t.....____,_ri
(c)
99.9 MHz 100.1 MHz i 100MHz
9)FM(I)
(b)
'"' 1111Mmmiiiww
i
·- mmi1mmmmmmi1 ·-
(d)
frequency modulation by a digital signal (Fig. 5 .Sb) is called frequency shift keying
(FSK) because information digits are transmitted by keying different frequencies (see
Sec. 7.8).
For PM:
k p . 8 1 .
_{; = fc + 2n
m(t) = IO + 4
m(t)
The derivative rii(t) (Fig. 5.5c) is zero except at points of discontinuity of m(t) where
impulses of strength ±2 are present. This means that the frequency of the PM signal stays
the same except at these isolated points of time! It is not immediately apparent how an
instantaneous frequency can be changed by an infinite amount and then changed back to
the original frequency in zero time. Let us consider the direct approach:
(/J pM (t) = A cos [w e t+ k p
m(t)J
= A cos [W e t+ im(t)]
_ {
A sin wet when m(t) = -1
- -A sin Wet when m(t) = 1
This PM wave is shown in Fig. S.Sd. This scheme of carrier PM by a digital signal is
called phase shift keying (PSK) because information digits are transmitted by shifting
the carrier phase. Note that PSK may also be viewed as a DSB-SC modulation
by m(t).
The PM wave 'PPM (t) in this case has phase discontinuities at instants where impulses
of m(t) are located. At these instants, the carrier phase shifts by n instantaneously. A finite
phase shift in zero time implies infinite instantaneous frequency at these instants. This
agrees with our observation about m(t).
The amount of phase discontinuity in cpPM (t) at the instant where rn(t) is discontinuous
is k p
rnd, where md is the amount of discontinuity in m(t) at that instant. In the present
example, the amplitude of m(t) changes by 2 (from - 1 to 1) at the discontinuity. Hence,
the phase discontinuity in 'PPM (t) is k p
md = (n /2) x 2 = n rad, which confirms our
earlier result.