TABLE OF CONTENTS As we mentioned in Sec. 3.1, angle modulation encompasses phase modulation (PM) and frequency modulation (FM) and refers to the process by which the phase angle of a sinusoidal carrier wave is varied according to the message signal. As we studied in Chap. 3, in amplitude modulation the spectrum of the modulated signal is essentially the translated message spectrum, and the transmission bandwidth never exceeds twice the message bandwidth. In angle modulation, the spectral components of the modulated waveform are not related in any simple fashion to the message spectrum. Furthermore, superposition does not apply (see Prob. 4.4), and the bandwidth of the angle-modulated signal is usually much greater than twice the message bandwidth. The increase in bandwidth and system complexity is compensated for by the improved performance in the face of noise and interference (see Chap. 8).
For angle modulation, the modulated carrier is represented by [see Eq. (3.1)]
where A and ? c are constants and the phase angle ?( t) is a function of the message signal m( t).
If we rewrite Eq. (4.1) as
where
then we can define the instantaneous radian frequency of x c( t), denoted by ? i, as
Note that when ?( t) = constant, then ? i = ? c.
The function ?( t) and d ?( t) dt are known as...
