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 respectively. In Frequency Modulation, the instantaneous frequency of the carrier is varied in accordance with the instantaneous amplitude of the message signal, while the carrier amplitude remains constant. If the message signal is (m(t)), an FM signal can be expressed as [ s_{FM}(t)=A_c\cos\left[2\pi f_c t+2\pi k_f\int m(t)dt\right] ] where (f_c) is the carrier frequency and (k_f) is the frequency sensitivity of the modulator. The instantaneous frequency is [ f_i(t)=f_c+k_fm(t) ] Therefore, a positive value of the message signal increases the instantaneous frequency, while a negative value decreases it. The amount by which the carrier frequency changes from its unmodulated value is called frequency deviation. For a sinusoidal message signal, [ m(t)=A_m\cos(2\pi f_m t) ] the FM signal can be written as [ s_{FM}(t)=A_c\cos[2\pi f_ct+\beta\sin(2\pi f_mt)] ] where (\beta) is the modulation index of FM. It is given by [ \beta=\frac{\Delta f}{f_m} ] where (\Delta f) is the maximum frequency deviation and (f_m) is the frequency of the modulating signal. The modulation index indicates the extent of frequency variation produced by the information signal. In Phase Modulation, the instantaneous phase of the carrier is varied directly according to the instantaneous amplitude of the message signal, while the carrier amplitude remains constant. The PM signal can be represented as [ s_{PM}(t)=A_c\cos[2\pi f_ct+k_pm(t)] ] where (k_p) is the phase sensitivity of the modulator. Thus, the phase deviation is directly proportional to the amplitude of the modulating signal. For a sinusoidal message signal, [ m(t)=A_m\cos(2\pi f_mt) ] the PM signal becomes [ s_{PM}(t)=A_c\cos[2\pi f_ct+\beta_p\cos(2\pi f_mt)] ] where (\beta_p=k_pA_m) represents the phase modulation index. In PM, the maximum phase deviation depends primarily on the amplitude of the message signal. FM