A discrete random process, X[n], is generated by repeated tosses of a coin. Let the occurrence of a head be denoted by 1 and that of a tail by - 1. A new discrete random process is generated by Y [2n] = X [n] for n = 0, ± 1, ± 2, … and Y[n] = X[n + 1] for n odd (either positive or negative). Find the autocorrelation function for Y[n].
Answer to relevant QuestionsA wide sense stationary, discrete random process, X [n] , has an autocorrelation function of . RXX [k] Find the expected value of Y[n] =(X [n+ m] – X [n– m]) 2, where is an arbitrary integer. Let s (t) be a periodic square wave as illustrated in the accompanying figure. Suppose a random process is created according to X (t) = s (t – T), where T is a random variable uniformly distributed over (0, 1). (a) Find ...Let X (t) be a wide sense stationary random process that is ergodic in the mean and the autocorrelation. However, X (t) is not zero- mean. Let Y (t) = CX (t), where C is a random variable independent of X (t) and C is not ...Let X (t) be a wide sense stationary Gaussian random process and form a new process according to Y (t) = X (t) cos (ωt + θ) where ω and θ are constants. (a) Is Y (t) wide sense stationary? (b) Is Y (t) a Gaussian ...Let X (t) be a Poisson counting process with arrival rate, λ. We form two related counting processes, Y1 (t) and Y2 (t), by randomly splitting the Poisson process, X (t). In random splitting, the i th arrival associated ...
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