Xt is a wide sense stationary stochastic process with

Question

X(t) is a wide sense stationary stochastic process with autocorrelation function R_X (τ ) = 10 sin(2π1000t)/(2π1000t). The process Y(t) is a version of X(t) delayed by 50 microseconds: Y(t) = X(t - t₀) where t₀ = 5 × 10^-5s.

(a) Derive the autocorrelation function of Y(t).

(b) Derive the cross-correlation function of X(t) and Y(t).

(c) Is Y(t) wide sense stationary? (d) Are X(t) and Y(t)jointly wide sense stationary