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UNIVERSITY OF TEXAS AT DALLAS Department of Electrical Engineering EE/TE 3350 Communications Systems Solutions 3 Amplitude Modulation Subjects: Amplitude Modulation Reading: Chapter 3 Solution 3.1 𝑚(?) = 2?𝑜? (2𝜋𝑓 𝑚 ?) = 2cos(1000𝜋?) 𝑓 𝑚 = 500 Hz, 𝑀(𝑓) = 2(0.5𝛿(𝑓 + 500) + 0.5𝛿(𝑓 − 500)) = 𝛿(𝑓 + 500) + 𝛿(𝑓 − 500) ?(?) = 𝑚(?) cos(20000𝜋?) 1 1/2
Solution 3.2 a) Let us write ?𝑜? 3 (?) = ?𝑜?(?)?𝑜? 2 (?) cos 3 (?) = ?𝑜?(?)(1 + ?𝑜?(2?)) 2 = 1 2 cos(?) + 1 2 cos(?) cos(2?) = 3 4 cos(?) + 1 4 cos(3?) ?(?) = 𝑚(?) cos 3 (2𝜋𝑓 𝑐 ?) = 𝑚(?) [ 3 4 cos(2𝜋𝑓 𝑐 ?) + 1 4 cos(6𝜋𝑓 𝑐 ?)] Note that the term 3 4 𝑚(?) cos(2𝜋𝑓 𝑐 ?) Is the desired signal, whose spectrum is centered at ±𝑓 𝑐 . The remaining term 1 4 𝑚(?)cos(6𝜋𝑓 𝑐 ?) is the unwanted term, which represents the modulated signal with carrier frequency 3𝑓 𝑐 . A bandpass filter with minimum bandwidth of 2B Hz centered at ±𝑓 𝑐 allows the passage of the desired term ?(?) = 3 4 𝑚(?) cos(2𝜋𝑓 𝑐 ?) But it suppresses the unwanted term. We can assume that passband gain of the filter is 1. b)
Solution 3.3 a) Let us denote the AM signal with ?(?) which is given by b) The overbar over the signals indicates the average of the corresponding signal. If we average the
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