EE320 Midterm Solution

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

EE320 Midterm Solution

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