Exercise 9. A random process X(t) has zero mean and autocorrelation function Rx (t, s) =...

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Exercise 9. A random process X(t) has zero mean and autocorrelation function Rx (t, s) = min(t. s). Consider the new process Y(t)= e'x (et). This process Y(t) is passed through an LTI system, of which the output Z(t) is related to the input Y(t) via Z(t) + 22(t)= = Y(t) + Y(t). dt dt (a) Show that Y(t) is wide sense stationary. (b) Find the autocorrelation function R(T). Exercise 9. A random process X(t) has zero mean and autocorrelation function Rx (t, s) = min(t. s). Consider the new process Y(t)= e'x (et). This process Y(t) is passed through an LTI system, of which the output Z(t) is related to the input Y(t) via Z(t) + 22(t)= = Y(t) + Y(t). dt dt (a) Show that Y(t) is wide sense stationary. (b) Find the autocorrelation function R(T).