Question

3. The system represented by the block diagram below modulates the message signal x(t) with a carrier wave c(t) to yield -(). The signal y(t) is generated by multiplying z() by the carrier wave c(t). c(t) c(t) y(t) z(t) The output signal,y(t), can be written as y(t)-C() × X() x C(t). Using the properties of a) Fourier Transforms, write Yi) in terms of Cjo) and Yj). [2 points] The Fourier Transform of x(t) is illustrated below. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2T b) If c cos(2xt), plot Z(jo) and Yja). [3 points] c) If c) cos(xt), plot Zjo) and Ym). [3 points] d) Comment on the differences between Yjø) in parts (c) and (d). Will it be possible to recover the original message signal from y() for both cases? Provide an explanation to justify your answer. [2 points]

Answer 1

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