# Question

Consider a random process of the form ,

X (t) = b cos (2πΨt + θ)

Where is a constant θ, is a uniform random variable over [0, 2π], and Ψ is a random variable which is independent of and has a PDF, fΨ (Ψ). Find the PSD, SXX (f) in terms of fΨ (Ψ). In so doing, prove that for any S (f) which is a valid PSD function, we can always construct a random process with PSD equal to S (f).

X (t) = b cos (2πΨt + θ)

Where is a constant θ, is a uniform random variable over [0, 2π], and Ψ is a random variable which is independent of and has a PDF, fΨ (Ψ). Find the PSD, SXX (f) in terms of fΨ (Ψ). In so doing, prove that for any S (f) which is a valid PSD function, we can always construct a random process with PSD equal to S (f).

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