Question: Let X t A t cos 0t where
Let X (t) = A(t) cos (ω0t + θ), where A(t) is a wide sense stationary random process independent of θ and let θ be a random variable distributed uniformly over . Define a related process Y (t) = A (t) cos((ω0 +ω1) t + θ). Show that X (t) and Y (t) are stationary in the wide sense but that the cross- correlation RXY (t, t + r), between X(t) and Y(t), is not a function of only and, therefore, Z(t) = X(t) + Y(t) is not stationary in the wide sense.
Relevant QuestionsLet X (t) be a modified version of the random telegraph process. The process switches between the two states X (t) = 1 and X (t) = –1 with the time between switches following exponential distributions, fT (λs) = λexp ...Two zero- mean discrete- time random processes, X [n] and Y [n], are statistically independent. Let a new random process be Z [n] = X [n] + Y [n]. Let the autocorrelation functions for X [n] and X [n] be Find RZZ [k]. Plot ...An ergodic random process has a correlation function given by What is the mean of this process? Let N (t) be a Poisson counting process with arrival rate. Find Pr (N (t) = k | N (t + τ) = m) Where τ > 0 and m≥ k. Suppose the power line in the previous problem has an impulse response that may be approximated by h (t) = te– atu (t), where a = 10s– 1. (a) What does the shot noise on the power line look like? Sketch a possible ...
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