final_spr06

final_spr06 - EE 562a Final Exam, 8 May 2006 WRITE YOUR...

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EE 562a Final Exam, 8 May 2006 WRITE YOUR NAME on the exam paper, and indicate if you are an ON-CAMPUS or DEN student. This exam is open book/open notes. You may use a simple calculator (i.e., not a scientiﬁc calculator), but you probably won’t need one. There will be two hours to complete the exam. Do all problems. Note that these problems have diﬀerent point values, and diﬀer widely in diﬃculty. You should look over all the problems before starting your work. Write all answers on the test paper. You may use scratch paper to do the problem, but the answer must be written with the problem. If you do work on scratch paper, and wish that work to be considered for partial credit, hand in the scratch paper along with the exam. Part I. Basic Concepts. For each question in this section, circle the best answer from the choices listed. Each problem has only one best answer. There is no partial credit on this section. (3 points each.) 1. Suppose that x ( u, t ) is fully ergodic. Then it must follow: (a) E { x ( u, t ) } is independent of t (b) lim T →∞ (1 / 2 T ) R T - T x ( u, t ) dt is independent of u with probability 1 (c) Any function of x ( u, t ) is mean ergodic (d) All of the above (e) Both (a) and (b) 2. For a continuous time random process x ( u, t ), which of the following gives a factorization of S x ( f ) = | G ( f ) | 2 = ( x 2 + 1) / [( x 2 + 4)( x 2 + 9)] in which both G ( f ) and 1 /G ( f ) are causal? (a) G ( f ) = ( x - i ) / [( x - 2 i )( x - 3 i )] (b) G ( f ) = ( x + i ) / [( x + 2 i )( x + 3 i )] (c) G ( f ) = ( x - i ) / [( x + 2 i )( x + 3 i )] (d) G ( f ) = ( x + i ) / [( x - 2 i )( x - 3 i )] 3. If A and B are both n × n circulant matrices, which of the following is true? (a) A and B have the same eigenvalues (b) A and B have the same eigenvectors (c) A and B commute (d) All of the above (e) Both (b) and (c) 4. Which of the following could be a covariance matrix K xx * ? (a) 2 0 2 0 - 1 0 2 0 2 (b) 1 i 0 - i 1 0 0 0 3 (c) 3 2 1 2 1 2 1 3 1 (d) 1 1 0 1 - 1 0 0 0 3

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EE 562a Final Exam 2 5. Which of the following could be the power spectral density of a real, mean zero, wide-sense stationary random process x ( u, t )? (a)
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This note was uploaded on 05/06/2008 for the course EE 562a taught by Professor Toddbrun during the Spring '07 term at USC.

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final_spr06 - EE 562a Final Exam, 8 May 2006 WRITE YOUR...

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