HW2Solutions

HW2Solutions - ECEN 661 - Modulation Theory Homework #2...

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ECEN 661 - Modulation Theory Homework #2 Solutions 1. (a). Start with (4.1-38): . Next compute the autocorrelation of the bandpass process, Since the last two terms are functions of both and , the original process will not be stationary unless and . Since the original process was stated to be stationary, we take these two identies to be true. Then . Using the two identities, we then get . (b) (since ). 2. nt () xt ω c t cos yt ω c t sin = Ent τ + [] Ext τ + ω c t ω c t ω c τ + cos cos Eyt τ + ω c t sin ω c t ω c τ + sin τ + ω c t cos ω c t ω c τ + sin τ + ω c t sin ω c t ω c τ + cos + 1 2 -- φ xx τ () φ yy τ + ω c τ cos 1 2 φ yx τ ()φ xy τ ω c τ 1 2 φ τ τ ω c τ 2 ω c t + cos 1 2 φ τ τ + ω c τ 2 ω c t + sin + sin = = t τ φ τ φ τ = φ τ φ τ φ τ == Ezt zt τ + Ex t jy t + τ + τ + + = φ τ τ j φ τ τ + + = τ + 0 = EV 2 Ez t zu t du d 0 T 0 T = t d 0 T 0 T 0 0 = 2 * t t d 0 T 0 T 2 φ zz ut t d 0 T 0 T 2 N o δ t d 0 T 0 T 2 N o t d 0 T 2 N o T =
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(a) , , , .
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HW2Solutions - ECEN 661 - Modulation Theory Homework #2...

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