Question

q.3

Question 31 Co points For a message signal a) Write express 1o", k1000 and i. For determining nderinite integrat of ) that ts, take te votue ot te ntrt at ons (do not skotc) ) n te o. Esti, nate the bandwidth of ф,.M0t) and .prM0t).

Answer 1

M (t) = 3 cos (2,000 t) + 7 cos (4000 pi t) phi_FM (t) = Ac cos (W_c t + 2 pi k_f integral^t_- infinity m (t) partial differential t) = 5 cos (10^6 t + 2 pi times 1000 pi integral^t_infinity (3 cos (2000 t) + 7 cos (4000 pi t)] = 5 cos (10^6 t + 2000 pi^2 [3 sin (2000 t)/2000 + 7 sin (4000 pi t)/4000 pi]) = 5 cos (10^6 t + 3 pi^2 sin (2000 t) + 7/2 pi sin (4000 pi t)) B_T = Maximum freq middot Deviation/Highest middot frequency of m (t) f_i = 1/2 pi d/dt (theta (t)] 1/2 pi partial differential/partial differential t (10^6 t + 3 pi^2 sin (2000 t) + 7 pi/2 sin (4000 pi t) = 1/2 pi (10^6 + 3 pi^2 middot 2000 cos (2000 t) + 14000 pi^2 cos (4000 pi t)] 10^6/2 pi + 3000 pi cos (2000 t) + 7000 pi