Question

Question A modulated voltage signal is given as: s(t) = 10(1 + 0.5cos(10?rt)) cos(106mt) volts. Plot the spectrum of the signal and calculate its bandwidth. b) Calculate the total signal power in dbm. c) If the message signal is a single-tone signal, explain if this is an AM-DSB-SC or an AM-DSB-C signal. What is the modulation efficiency? d) The signal s(t) is passed through the following system. Find the output mout(t) as a function of time and its Fourier transform, Mout(f). 2 s(t) vlt) LPF mout(t) -2KHz 0 2KHz cos(10%)

Answer 1

Given: s(t) = 10(1+0.5 COSC 1021Tt)) cosC1ofert) a spectrum of the signal slf) Ach Аси ACA 4 4 4 fathm fc-fm -fcfm fc fetfm where A-10 M=0.5 7 fc = { 0 Hz, from the 500KHZ, 250 Hz sets 15 1-25 1-25 1-25 1-25 a& 500k-50 5ook 500k+50 - 500kato -500k -50+5 Band width fc+fm - (fc- fm) Band width q fm - 2 (50) Band width = 100Hz

b) total signal power Ptotal こ Pelltu Ac2 2 (1+ 10 (1+ (0.5) = 56.25W power in dBm Ptotal lolog (5625) dBm Ptotal 475 dBm We can observe carrier present in the spectrum of sct) therefore AM-DSB-C modulation efficiency (1) - it is u2 27 128 xico u=0.5 100 = 11.1% ma 2+0.952tloo

modulation efficiency (1) = 11.11% vct): sct) cos(lot) 2 VCt) = 1001+0.5 cos Ciofert) cos? Ciobots = 10(1+0.5 (S(10?xt) (1+60562 Mobey = 5 (1+0.506 (10*nt)) (1+601(21T xlofty when Vct) is passed through WPF only frequencies less than 2kHz are allowed mout (t) = 5(1+0.5COS (10?mt)) x2 #5003 (tort) mout cts = 10+ [SCP-59) +014+597 Mout (fy - 108(f) + Mout(f). 2.5 50 -50