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Unformatted text preview: v ( t ) is a given real signal such that V ( f ) = 1 for  f  ∈ [1 , 2] and V ( f ) = 0 elsewhere. Suppose you treat the random process X t as a jamming signal that you are free to design (as an adversary). The design objective is to minimize the bestcase SNR at the output of the receiver ( bestcase here means maximum over all possible receiver designs). The design constraint is that you have only a ﬁxed amount of power P to allocate to your jammer. Describe your design of the jamming signal. (It sufﬁces to design the power spectral density S X .) 5 6 4. (15 pts.) Let B be a Bernoulli random variable taking values on { , 1 } . Deﬁne the discretetime process X 1 , X 2 , . . . by X t = (1) B + t , t = 1 , 2 , . . . . Let p = P { B = 0 } . a. For what values of p is the process X t strictly stationary? b. For what values of p in part a is the process also ergodic? Explain fully. 7 8...
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 Spring '08
 Staff
 Signal Processing, Probability theory, pts, Stationary process, random process Xt, discretetime process X1

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