EE 511 Problem Set 8 1. Let X t be a W.S.S. random process and let Y t = X t cos 2 πf c t and Z t = X t cos (2 πf c t + Θ) where Θ is uniformly distributed in [0 , 2 π ] and independent of X t . Show that Y t is wide-sense cyclostationary and Z t is W.S.S. 2. Let X t (transmitted signal of a communication system) be a random process deFned as follows: X t = ∞ s n =-∞ A n p ( t − nT − T d ) , where A n are binary random variables (that take values +1 or -1 with equal probability) such that E [ A n A n + k ] = R A ( k ), T d is a random variable independent of A n for all n and is uniform in [0 ,T ], p ( t ) is the pulse shape used for transmission, and T is a constant. a) Determine the auto-correlation of X t in terms of R A ( k ) and the pulse shape
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Probability theory, Stochastic process, Stationary process