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Consider a pair of random processes x(t) and Y(t) that are related to a wide-sense stationary (WSS) process W(t) as follow: x(t) = W(t)cos(2πf꜀ t + Θ) Y(t) = W(t)sin(2πf꜀ t + Θ) Where Θ is uniformly distributed over (0, 2π), and also independent of W(t). A) Find the cross-correlation R_xy(τ). B) Find the autocorrelation of x(t). C) Find the power spectral density of Y(t). D) In what condition x(t) and Y(t) will be orthogonal?
Sagot :
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