Question

A carrier signal c(?) = ? cos(??) is modulated by a single-tone signal ?(?) = ? ???(??) to form the AM signal: s(t)= [? + ????(??)]???(??), where ? = 10, ? = 2, ? = 1000 ??, ? = 50 ??. a- Obtain an expression for the sidebands of ?(?). b- Sketch ?(?) c- Sketch the spectra |?(?)|, |?(?)|, |?(?)| against f. d- Calculate the modulation index (m) e- What bandwidth is required to transmit the AM signal. f- Show that the sideband power to the power in the modulated wave is equal to   

Answer 1

Giuon corrion signal ccé) - A cont.) whore = A caug41) A = 10 t = 1000 Hz Then Cee) = 10 collar tegut) Similanly me) = Acout) A casca.lift) Whore f = solte mu) = 2 cos (21 sat) 2 then 4 ربر کو Am signal 50) = (4+4 cas ext)) cos ut [10 +acos (an 50€)] ces can 10rp ) 10 (1+0.2, cas la miss 4]] ces can listok) The general form of Am single tone zignal is Sw) = Ac Est le cas canfmt)j cesar tet) modulatim index kellene l= = m = m= 0.2 de= corriere enpletade = 10 fm = 50tte fe= 1000 Hz.

CQS (A+B) + las (4-3) las SC) = 10 [1+0.2 les art so t)] cas (att imot) 10 cos art 1 rook + 2 ces (artist) LOJ 211 sot kle know cas A. COMB a, Then Sat) = 10 case T 1000k)+ X[ ces at (ovo +90) E + cas att (1800-50) t] 2 are the locas (Q 11000 ) + casar loso t) + cas (277 950) where cas (21 1050 t) + cos(at 950€) Sideband of set) cas (at 1050&) is Uppek side band (USB) cas Cart 950 €) is Lawen side bend (LSB)

(6) Sketch of sct) Envelope el wyt on (72S 8 AC-Am Ac=10 Am=2

Francier Transforms of Owot e mct)=cas Wort 2. cas Wol is - Twol f e 2 2 f[emaet J - 21 600-ws) = 77 80w-wo) So f [ casuot २ TWot Где 2 1 8 (wtao) Trow fwo 2 2 IT & CW-wg) + T8 (W two) M (W) T86w-Wo) ttr (w two) MCH) 118 <-lo) + Tatto ZIT

MGH), 501-6) +504 +40) 2 Speettern of Mcd) es Almeldi 71 (te) given mct) = a las 2150 t) Then MCA)=2864-50) + 2864 +50) 2 2 544-50) +506 +50) Se, the speeftern of IMCL)! is MC) > f Cha 50 - 50 Samilarly COC) = 10 cascani trot) c(t) = 10861- (TO) +10511+ leto) 2 5864-170) +560! +70) So, the spectrum of leed) I i 2 15 Alee!!!

Samilarly SCL) = 10 cos Cartierot) + cos car 1000 €) + cas (21 950 €) SCH) = 5814-16) +55(++lroo) t 567-1050) +55(++1050) + **(+-250) + (+ +950) So, the speefterm of 1s(f) / is Iscell A is ak a į ah - 1000-950 -1050 950 1600 1050 f (Hz)

(d) Modulation inden 0.2 , as per the general teten af Am signal . Modulation inden (m) = Am ale Ac حياة 10 0.2 ce) Bandouldth required to transmit the AM signal is a.fm - 28.50 = 10Hz Ok, from Speefrem it is shawn that 1050 – 950 roofz. (+) Power 2 Vieme R R=12 fore normalize powere T 2. St Act) at Viens = ... reft) is any Signal. for casine signal Vems = Vm < Peak amplitude. vã Sideband Pawek FSB PusB + PLSB 1 2 3 + 1 ces QT 1050 €) } Both the case peak amplitude cas (21 950.6) 2. = 2 watt V2 USB = LSD = is 1,