Question

4.5-1 A modulating signal m(t) is given by (a) m (t) = cos 1001 (b) m(t)cos 100r2 cos 300t (c) m(t)cos 100r cos 500 In each case: 1) Sketch the spectrum of mt) (ii) Find and sketch the spectrum of the DSB-SC signal 2m(t) cos 1000 ii) From the spectrum oblained in (ii), suppress the LSB spectrum to obtain the USB spectrum. (iv) Knowing the USB spectrum in (ii), write the expression Pusn (t) for the USB signal. v) Repeat (ii) and (iv) to obtain the LSB signal Pasn).

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Answer 1

W(t) = cos 100t = e^- j 100t + e^- j 100t/2 M(t) = 1/2 delta (t - 100) + v/2 delta (t + 100) PSB - SC signal D(t) = 2 w(t) cos 1000t = 2 cos 100K cos 1000t = cos (1100t) + cos 9 900t) = e^- j 1100t + e^j 1100t/2 + e^- j 900t + e^j 900t/2 s(t) = 1/2 {delta (t + 1100) + delta(f - 1100) + delta (f + 900) + delta (f - 900)] LSB frequencies are plusminus 900 HZ suppress LSB spectrum s_1(f) = 1/2 [delta (f + 1100) + delta (f - 1100)] \r\n phi_USB (t) = 1/2 [delta (f + 1100) + delta (f + 1100)] phi_USB (t) = 1/2 [e^- j1100t + e^j1100t] phi_USB (t) = cos 1100t phi_USB (t) = 1/2 [delta (f + 900) + delta (f - 900)]