Question

Simplify the following identity used in an electrical engineering text to represent the received AM signal function. Note that A, 0, 0, are constants and M (1) is a function of time, r(t) = (A + M (0)) cos Wet+I cos(@c + wat t. X O r(t) = ((A+M()) + I cos wst) cos oct +I cos wat Or(t) = ((A+M(O)) +I cos wst) cos wet+sin wat sin wct r(t) = ((A+M(t))+I sin wat) cos wet+I sin oct cos out r(t) = ((A+M()) - 1 sin wat) cos oct +1 sin wet cos wat Or(t) = ((A+M (0) + I cos wat) cos met1 sin wat sin wet 18.P.Lathi, Modern Digital and Analog Communication Systems, 2nd ed. (OUP, 1989), page 269. O

  

Answer 1

M(t) = (A+m (t)) os wit + I wos (We + Walt (A + m(t)) cos wat & I (ws (Wet) ws (wat) - sin(Wit) sin(wat) A cos wet + mct) was welt) + I was (oct) costwat) - I sin (Wet) sin(Walt) - COS (W2+)CA + m(t) + I wos(at)) - I sin (wet) sin(wat) [A + At m(t) + I was (wat) at)] cos (out) – I sin (wet) sin(wat) le option © is comed