Two random processes X(t) and Y(t) are given by
X(t) = Acos(2ωft + θ)
Y(t) = Asin(2ωft + θ) where A and θ are constants and ω is a uniform random variable over [0, 2π]. Find the following:
Mean mx(t) = E[X(t)]
Mean my(t) = E[Y(t)]
Autocorrelation Rx(t,t + Ï„) = E[X(t)X(t + Ï„)]
Autocorrelation Ry(t,t+Ï„) = E[Y(t)Y(t+Ï„)]
Cross correlation Rxy(t,t + Ï„) = E[X(t)Y(t + Ï„)]
Cross correlation Ryx(t,t + Ï„) = E[Y(t)X(t + Ï„)]