Question

4.4-6 An LSB signal is demodulated coherently, as shown in Fig. P4.4-6. Unfortunately, because of the transmission delay, the received signal carrier is not 2 cos Wet as sent, but rather, is 2 cos[wc + Aw)t + 8). The local oscillator is still cos wct. Show the following. (a) When 8 = 0, the output y(t) is the signal m(t) with all its spectral components shifted (offset) by Ao. Hint: Observe that the output y(t) is identical to the right-hand side of Eq. (4.20a) with Wc replaced with Δω. (b) When Aw = 0, the output is the signal m(t) with phases of all its spectral components shifted by 8. Hint: Show that the output spectrum Y(f) = M)eid forf > 0, and equal to M (f)e-j8 when f <0. (c) In each of these cases, explain the nature of distortion. Hint: For part (a), demodulation consists of shifting an LSB spectrum to the left and right by wc + Aw and low-pass-filtering the result. For part (b), use the expression (4.20b) for CLSB(1), multiply it by the local carrier 2 cos (Wet + 8), and low-pass-filter the result. Problems 201 Figure P.4.4-6 PLSB (1) y(1) Low-pass filter 2 cos [(wc + A)1 + 0]

Answer 1

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