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20072ee132A_1_hwk2_sol

# 20072ee132A_1_hwk2_sol - EE132A Spring 2007 Prof John...

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EE132A, Spring 2007 Communication Systems Prof. John Villasenor Handout# 7 TA: Choo Chin (Jeffrey) Tan Homework 2 Solutions 1. (a) To avoid over-modulation, use 1 μ . (b) The plots of ( ) s t and ( ) v t are shown in Figure 1. Overmodulation occurs in ranges 1 3 2 3 m m f f f / < < / , 4 3 5 3 m m f f f / < < / , and so on for the following periods. Figure 1. v(t) for problem 1(b) (c) For ( ) cos 2 m m m t A f t π = , ( ) M f is given by [ ] ( ) ( ) ( ) 2 m m m A M f f f f f δ δ = - + + Figure 2 shows a plot of ( ) M f . Figure 2. M(f) for problem 1(c)

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To obtain V ( f ) we split the function from part (b) into two parts: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 2 3 1 2cos 2 rect * 2 2 sinc 3 3 2 2 sinc 3 3 m c m k m m m k m m k f v t A f t w t t k w t t f k W f f t k f f k t k f π δ δ δ =-∞ =-∞ =-∞ = + = -   = -       = -     The second function is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1 2 2 2 1 2 1 3 1 2cos 2 rect * 1 1 sinc 3 3 1 sinc 3 3 1 1 sinc 3 3 m m m m c m k m j f f m m k m m f j f m k m k m k f f v t A f t w t t k w t t f W f e f f
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