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ee320 midterm solution

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                                   H (f ) =| H (f ) | e jβ(f )  f  = 0, 500 and 1500 Hz.  |  H (f )  |   β (f )    x 1 (t) = 8 , X 1 (f ) = 8 δ (f ), Y 1 (f ) = 4δ (f )  y 1 (t) = 4    x 2 (t) = 4sin(1000πt), X 2 (f ) = 2e −j π 2 δ (f  − 500) + 2e j π 2 δ (f  + 500), Y 2 (f ) = 2e −j(500φ+ π 2  ) δ (f  − 500) + 2e j(500φ+ π 2  ) δ (f  + 500)  y 2 (t) = e −j(0.5φ+ π 2  ) e j(2π500t) + e j(0.5φ+ π 2  ) e −j(2π500t) y 2 (t) = 2sin(1000πt − 0.5φ)      x 3 (t) = 10cos(3000πt), X 3 (f ) = 5δ (f  − 1500) + 5δ (f  + 1500), Y 3 (f ) = 5e −jφ δ (f  − 1500) + 5e jφ δ (f  + 1500) y 3 (t) = 5 e −jφ e j(2π1500t) + 5e jφ e −j(2π1500t) y 3 (t) = 10cos(3000πt − φ)    x 1 (t) = 8  

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