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Angle modulation is a type of continuous-wave modulation in which the information signal is used to vary the angle of a high-frequency carrier wave rather than its amplitude. The amplitude of the carrier remains constant, while either its frequency or phase is varied according to the instantaneous value of the message signal. The two principal forms of angle modulation are Frequency Modulation (FM) and Phase Modulation (PM). Both techniques are widely used in communication systems because constant carrier amplitude provides better immunity to amplitude noise and allows efficient use of nonlinear power amplifiers. A sinusoidal carrier can be represented as [ c(t)=A_c\cos(\omega_c t+\phi) ] where (A_c) is the constant carrier amplitude, (\omega_c) is the carrier angular frequency, and (\phi) is the phase angle. In angle modulation, the amplitude (A_c) remains unchanged, while the instantaneous angle of the carrier is varied by the message signal. The general expression for an angle-modulated signal is [ s(t)=A_c\cos[\omega_c t+\theta(t)] ] where (\theta(t)) represents the time-varying phase deviation produced by the information signal. The instantaneous frequency of a signal is related to its instantaneous phase by [ f_i(t)=\frac{1}{2\pi}\frac{d}{dt}[\omega_c t+\theta(t)] ] Thus, angle modulation can be achieved either by directly changing the instantaneous frequency of the carrier or by changing its phase. These approaches result in FM and PM _____ ___ _________ ___ ______ __________ _____ ______ __________.
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