5. Let T > 0 be an arbitrary number and let X(t) be a process that satisfies: ux(t + mT) = px(t) Cx(tı + mT, t2 + mT) =

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5 Let T 0 Be An Arbitrary Number And Let X T Be A Process That Satisfies Ux T Mt Px T Cx Ti Mt T2 Mt 1 (51.5 KiB) Viewed 69 times

5. Let T > 0 be an arbitrary number and let X(t) be a process that satisfies: ux(t + mT) = px(t) Cx(tı + mT, t2 + mT) = Cx(tı, t2) for any integer m (this process is called Wide sense cyclostationary process). Define Y(t) 4 X(t + o), where ~ U[0,T] (uniformly distributed between 0 and T) and independent of X(t). (a) Show that y(t) is WSS. (b) Assume that, in addition, X(t) satisfies: m FX(tu+mT),X (ta+mT)...X(tm+mT) (21, 22, ..., In) = Fx (t1),X(t2)...X(tm) (21, C2, ..., In) Show that in this case Yt) is stationary. Hint: use the characteristic function.