EE 278 Final: EE278 Final Exam Summer 2017
9 Jan 2019
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The exam is closed book and closed notes except for one sheet (two sides) of notes. Points will be subtracted for correct answers with no reasoning, partial credit will be given for answers that are well reasoned even if the nal result is wrong. Useful formulas: trigonometric identities: sin(x) sin(y) = cos(x) cos(y) = sin(x) cos(y) = 2 (cos(x y) cos(x + y)) (cos(x y) + cos(x + y)) (sin(x + y) + sin(x y)) ej = cos( ) + j sin( : discrete-time fourier transform: [n m ] anu[n] (0 < |a| < 1) u[n] ej2 f0n: continuous-time fourier transform: 1 e j2 f + 1 k= (f f0 k) Time domain x(t) fourier transform x(f ) x(t) (f a) ej2 f a x(at t0) |a| e j2 f t0x (cid:0) f a(cid:1) where u(t) = 1{t 0: kalman filter recursion: Xn+1 = xn + wn, wn n (cid:0)0, 2. Yn = hxn + zn, zn n (0, 2.
