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In Sections 8.1 and 8.2, we analyzed the sinusoidal amplitude modulation and

Chapter 8, Problem 8.21

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QUESTION:

In Sections 8.1 and 8.2, we analyzed the sinusoidal amplitude modulation and demodulation system of Figure 8.8, assuming that the phase 8 c of the carrier signal was zero. 8.22. cos(5wt) (a) For the more general case of arbitrary phase 8 c in the figure, show that the signal in the demodulation system can be expressed as 1 1 w(t) = 2x(t) + 2x(t)cos(2wct + 28c). (b) If x(t) has a spectrum that is zero for lw I 2:: w M, determine the relationships required among w co [the cutoff frequency of the ideallowpass filter in Figure 8.8(b)], We (the carrier frequency), and WM so that the output of the lowpass filter is proportional to x(t). Does your answer depend on the carrier phase 8 c?

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QUESTION:

In Sections 8.1 and 8.2, we analyzed the sinusoidal amplitude modulation and demodulation system of Figure 8.8, assuming that the phase 8 c of the carrier signal was zero. 8.22. cos(5wt) (a) For the more general case of arbitrary phase 8 c in the figure, show that the signal in the demodulation system can be expressed as 1 1 w(t) = 2x(t) + 2x(t)cos(2wct + 28c). (b) If x(t) has a spectrum that is zero for lw I 2:: w M, determine the relationships required among w co [the cutoff frequency of the ideallowpass filter in Figure 8.8(b)], We (the carrier frequency), and WM so that the output of the lowpass filter is proportional to x(t). Does your answer depend on the carrier phase 8 c?

ANSWER:

Step 1 of 5

(a)

Representing the modulated signal as shown,

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