Two random processes are given by X (t) = n (t) + A cos(2f 0 t +

Two random processes are given by

X (t) = n (t) + A cos(2πf₀t + θ)

and

Y (t) = n (t) + A sin(2πf₀t + θ)

Where A and f₀ are constants and θ is a random variable uniformly distributed in the interval [-π, π). The first term, n (t), represents a stationary random noise process with auto correlation function R_n(τ) = BΛ(τ/ τ₀), where B and τ₀ are non-negative constants.

(a) Find and sketch their auto correlation functions. Assume values for the various constants involved.

(b) Find and sketch the cross-correlation function of these two random processes.