Question

HIM(6) met VC) 2 LPF BW-B Amplifier (x2) 1 ܙܟܠ/ fcos (21fct) -fe - B I fc (A) 544) 23 2B BPE etc BW:B + ylt) A message signal n4) has a spectrum (M(f) | as given above. This sipnal is led to the system given above (rijoht), (a) Draw the spectrum of Vlt). (6) Draw the spectrum of output sipral y (t). (c) Find the total power of the output signal, yct)

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Answer 1

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Sol:- Signal m It has Spectrum Incel 1 IMEI 2 1 -B O -fe 28 B fc 28 VID ott mit) ♡ LPF BW=B Amplifier (x2) Cosallfat Sit) rit) BPF af BW = 2B y (t) la We know V (t): m (t) Coszt fet that is and according to madulcation property of Fouriey - transhum prt). Cos 211 fot (f:I[P6+ Po) + PCP -fo] theregore Mit) = m(t) cosalift Fly 1 [M(ft fc) + MH-fo]] 2 2 VH) ALL V(A) so spectrum IV (A) = I [MLf+fc) + M (f- fc) og VLE. 2

CLASSTIME/Pg. No. Date / VE! So 1 1 112 1/2 -fc ol -B B fc 2pc 2f T2B F 2B 2B 2B Now (t) passes through LPF f (BW = BW = B) to to give g' (t) and gift) is amplified by 2. to give rit) Ipf will only pass the portion of V(f) cenderes around origines and have bandwidth B LPP 1 B 80 &lt) L. R (P) (spectrum of r(t) I RIFT B 0 B Vit) passes through Bpf (band pass filter) Centered around fc with bandwidth 2B I BPF 1 76

Date So is SIt F-T $(A) 15(el 1 - fc fo 23 2B Now, 3 () - = 0 IU) +547) Taking fourier transfoom of y It) and using linearity property of f. i spectrum of Y (P) = R(D) + s (f) y (t) (B) 2 2 2 4 -fo B 0 B fc 2B 28 » We (c) Total Power of yt know for a energy signal Energy finite power O lzero) so using parsevals energy theorem energy y y It is

E J 11 (f) 12 d ♡ so are I energy is arua of lY (f) 12 graph. there 3 triangular wave form whose energy is given by Ixbxh 6= base of triangle 3 h = height of triangle. ) - { x 2B X1 + $ X2B X2 + { x2BX/ 3 E = Y X2B = 3 8B 3 J 80, energy is finite, the averge power will be zero. energy signal Y It) is power of y It will be zero.