a) autocorrelación de Z(t)
E[Z(t_1)Z(t_2)] = E[(X(t_1) - Y(t_1))(X(t_2) -Y(t_2))] = E[X(t_1)(X(t_2) - X(t_1)Y(t_2) - Y(t_1)X(t_2) + Y(t_1)Y(t_2)] = E[X(t_1)(X(t_2)] - E[X(t_1)Y(t_2)] - E[Y(t_1)X(t_2)] + E[Y(t_1)Y(t_2)] = R_X(\tau) - R_{XY}(\tau) - R_{YX}(\tau) + R_Y(\tau)b) Densidad espectral de potencia de Z(t)
Sz(f) = F[R_X(\tau)] - F[R_{XY}(\tau)] - F[R_{YX}(\tau)] + F[R_Y(\tau)] = S_X(f) - S_{XY}(f) - S_{YX}(f) + S_Y(f) = S_X(f) - S_{XY}(f) - S_{XY}^* (f) + S_Y(f) = S_X(f) - H(f) S_{X}(f) - H^* (f) S_{X}(f) + S_Y(f) = [1 - H(f) - H^* (f) + |H(f)|^2] S_X(f) = [1 - 2Re[H(f)] + |H(f)|^2 ] S_X(f) Sz(f) = |1 - H(f)|^2 S_X(f)