problem_set5 - EE 511 Problem Set 5 Due on 17 October 2007...

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Unformatted text preview: EE 511 Problem Set 5 Due on 17 October 2007 1. An experiment has four equally likely outcomes 0, 1, 2, and 3, i. e., S = { , 1 , 2 , 3 } . If a random process X t is defined as X t = cos (2 πst ) for all s ∈ S , then (a) Sketch all the possible sample functions. (b) Sketch the marginal CDF’s of the random variables X , X . 25 and X . 5 . (c) Determine the conditional pmf of X . 25 given that X . 5 = − 1. (d) Determine the conditional pmf of X . 25 given that X . 5 = 1. 2. a) Determine the auto-correlation function of the random process X t = A cos (2 πf c t + Θ), where A and f c are constants, and Θ is uniformly distributed in [0 , 2 π ]. b) Can you come up with a different pdf for Θ such that X t remains wide-sense stationary (W.S.S)? 3. A random process Y t is defined as Y t = X t cos (2 πf c t + Θ) where X t is a W.S.S random process, f c is a constant, and Θ is a random variable independent of X t and uniform in [0 , 2 π ]. a) Is Y t W.S.S? b) If Y t is defined as Y...
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problem_set5 - EE 511 Problem Set 5 Due on 17 October 2007...

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