# m1_practice - ECE 562 Fall 2011 PRACTICE EXAM 1 50 pts...

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ECE 562 Fall 2011 PRACTICE EXAM 1 – 50 pts total (7:00 – 8:30 PM) Instructions : This is a closed book exam, but you are allowed to use 1 sheet of notes (8.5” × 11”; both sides). Don’t forget to put your name on the exam book. Good luck! 1. (15 pts total) True or False. Determine if the following statements are True or False. You need to provide a brief justification for your answer to get credit. (a) The complex baseband representation of 2 cos( πt ) cos(2 πf c t ) is cos( πt ). (b) If X = X I + jX Q is a proper complex random variable then Var( X I + X Q ) = Var( X I ) + Var( X Q ) (c) The maximum likelihood detector always minimizes the error probability. (d) For PSK modulation on an AWGN channel, the Intelligent Union Bound and Nearest Neighbor Approximation always coincide. (e) For 4-ary orthogonal modulation, P b = P e / 2. 2. (11 pts total) Gram-Schmidt. Consider the following signal set. t s 3 ( t ) 0 s 1 ( t ) s 2 ( t ) 1 2 t 1 1 t 0 0 1 1 2 t 0 1 1 2 1 s 4 ( t ) (a) (4 pts) Find an orthonormal basis for the span of this signal set. (Think before you answer since the G-S solution is not unique.)

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• Fall '08
• PRAMODVISWANATH
• pts, Quadrature amplitude modulation, Phase-shift keying, nearest neighbor approximation, V.V. Veeravalli

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