Question

1. DSC-SC Modulation. Consider a message signal m(t) = 3 sinc(10t) this is applied to a product modulator with a carrier wave c(t) = 2 cos(100nt). (a) (5 points) Find and plot the Fourier transform S(f) of the DSB-SC modulated signal s(t). (b) (5 points) What is the bandwidth of s(t)? (c) (5 points) The signal s(t) is next applied to filter h(t), the output of the filter is named y(t). Now assume that I $2/300, If|< 30, H(f) = 3, 30 < \f | < 70, L \f> 60. Find and plot the Fourier transform Y(f). (d) (10 points) The signal y(t) is then applied to a coherent demodulation. Find the optimum low pass filter so that the output of the coherent demodulation vo(t) = m(t)

Answer 1

given m(t)- 3 Sinc (1ot) , CCt) = 2cos(100TT+) SIt) = Mit) c(t) 3 sinc(ot) 2 cos (1061t) 6 Sinc (tot) cos (00 TTt) Fousier Trans form of mt)= MCf) * St): G stnc fot) Cas (1o0Tt) = (5 Sinc(iot) 105 mrt Applying fourier Trnnsform. (3 Sinc(lot) 200siooTTt %3D fourier Transfom of met) ces 2I ft = 4 [M(F-f)+ M(ft fc) SIf) = M(f- fc) + MCf+ fc)] %3D SCf) = M(f-50) +MCf i50) . F-T of Sinc at - Set(). MCf)- 3. Kect () F.T of Sincat lal But 1o So, Yect (f-50) + 0-3 Yect (fts0) scf)= 0.3 10 H(f) L0.3

Scf) 0.3 >f 55 -55 -45 45 Bandwidth of DSB-SC Signal = 2 (hghest message Signal fraquenay) = 2X5 Bandcoicth = 10 HZ SIt) hct) y(t) -> YA) = S(f) HCf) %3D H(f) 30 - 30 60 70 -70 -60 Y(H) 45 55 -55

Coherent demadubtor L(t) LPF Y(H) product plt) modulator CH) P(f)= yCf) C(f) Cif)- 8(+-50) + 8(f+50) PCf)= y(f-50) + y(f t50) PH) 0.9t0.9 -95 -5 95 105 p(f) 1.8 -95 -5 -l05 95 105 The cptimum louw pass filler to generate mt) LIf) -5