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.
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