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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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