Question: Let the sample functions of a random process be given by X(t) = A cos 2Ïf 0 t where Ï 0 is fixed and A

Let the sample functions of a random process be given by

X(t) = A cos 2Ï€f0t

where ω0 is fixed and A has the pdf 

e-a? /20, fA (a) = V2πσ, τσ α

This random process is passed through an ideal integrator to give a random process Y(t).

(a) Find an expression for the sample functions of the output process Y(t).

(b) Write down an expression for the pdf of Y(t) at time t0. Note that sin 2Ï€f0t0 is jsut a constant. 

(c) Is Y(t) stationary? Is it ergodic?

e-a? /20, fA (a) = V2,

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